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SMATICAI 



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LIBRARY OF CONGRESS. 



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OITED STATES OF AMERICA. 




The Full Moon, from a Photograph. 



ECLECTIC EDUCATIONAL SERIES 



ELEMENTS 



OF 



ASTRON OM Y 



WRITTEN FOR THE MATHEMATICAL COURSE OF 

JOSEPH RAY, M. D. 



SELIM H. PEABODY, Ph. D., LL. D. 

M 
Regent of the Illinois Industrial University 



NEW EDITION 




I JAN 16 1! 

VAN ANTWERP, BRAGG & CO 



CINCINNA 11 



.\ YORK 



Eclectic Educational Series. 



O^ 



High School and College Course of Study. 



v* 



White's New Complete Arithmetic. 
Ray's New Higher Arithmetic. 
Ray's New Algebras. 
Ray's New Astrono??iy. 
Eclectic School Geometry. 
Schuyler's Complete Algebra. 
Schuyler's Elementary Geometry. 
Schuyler's Principles of Logic. 
Schuyler's Psychology. 
Duffei's (Hennequm' s) French 

Method. 
Duffet's Erench Literature. 
Hepburn's English Rhetoric. 



Eclectic Complete Book-keeping. 
Thalheimer' s Historical Series. 
Norton's Natural Philosophy. 
Norton's Elements of Physics. 
Norton' s Chemistry — Co?nplete. 
Eclectic Physiology. 
Gregory's Political Economy. 
Andrews's Manual of the Consti- 
tution. 
Bartholomew' s Latin Series. 
Holbrook's First Latin Lessons. 
Kidd's New Elocution. 
Murdoch's Analytic Elocution. 



DESCRIPTIVE CIRCULARS ON APPLICATION. 



Entered according to Act of Congress, in the year 1869, by Wilson, Hinklc &■> 

Co., in the Clerk's Office of the District Court of the United 

States, for the Southern District of Ohio. 



Copyright, 1884, by Van Antwerp, Bragg & Co. 



ECLECTIC PRESS: 
VAN ANTWERP, BRAGG & CO. 



PREFACE 



In this work I have endeavored to describe and explain 
the. Mechanism of the Solar System and of the Stellar Uni- 
verse. Though written for pupils in the higher grades of 
public schools, it may be found useful in institutions of still 
higher rank, and as a foundation for more extended research 
by the private student. 

Although well aware that the rigid principles of mathe- 
matics and mechanics form the sole foundation of high 
astronomical attainment, I have carefully avoided abstruse 
mathematical demonstrations. Most who study Astronomy 
desire an accurate knowledge of facts and principles, but 
need neither for mental culture nor for practical use such a 
mastery of methods as should fit them to become even ama- 
teur astronomers. For such, I have aimed to furnish needed 
information and instruction. 1 have assumed that my readers 
know only the simplest principles of geometry and algebra, 
and the plainest facts of mechanics and physics. The vest 1 
have endeavored to supply as needed. 

The liberality of Publishers has enabled me to insert an 

unusual number of illustrations. Of the telescopic views, 

selected from the best authorities, some have lately found 

their way into American text books; others appear now tor 

(iii) 



IV ELEMENTS OF ASTRONOMY. 

the first time. The beautiful experiments of Foucault on the 
Rotation of the Earth, of Fizeau on Light, and of Plateau on 
Rotation, have not been described hitherto in works of this 
grade. The same is true of the elegant apparatus of Bache 
for measuring base-lines, reference having usually been made 
to the clumsier machinery of the English or French. Many 
of the diagrams are new, the fruits of hard work in the class- 
room. 

If the omission of the figures of men, animals, and serpents 
from the star-maps seems to any a questionable innovation, I 
have to say that my own experience as a teacher long since 
convinced me that those monstrosities hinder rather than 
help; and that my practice is sanctioned by Arago, Herschel, 
Lockyer, Proctor, Guillemin, and others, foremost astronom- 
ical writers of the present day. 

The Circumpolar Map is drawn on the equidistant projec- 
tion, the increase in polar distance being always equal to the 
increase in circular arc. The Equatorial Maps have for base- 
lines the meridian and the equinoctial — circles easily found, 
and always in the same position relative to the observer. 
The projection is the Polyconic, adopted by the U. S. Coast 
Survey for terrestrial maps, and now first used, so far as I am 
informed, for astronomical maps. Each tenth declination- 
parallel is assumed to be the base of a cone, tangent to the 
sphere in that circle; the spherical surface between that and 
the next higher parallel is projected into the conical surface, 
which is then developed upon a plane. As the maps extend 
but 30 on either side of the meridian, it is believed that 
the distortion, caused when a spherical surface is represented 
on a plane, is reduced to a minimum. The stars have been 
carefully platted from Proctor's Tables. 



PREFACE. v 

I am indebted to the courtesy of the Director of the U. S. 
Naval Observatory, and to the Assistant in charge of the 
Coast Survey Office, at Washington, for valuable information ; 
to Prof. Henry Morton, Ph. D., of the Franklin Institute, 
Philadelphia, through whose unsolicited kindness I am able 
to present the superior engraving of the moon, reduced from 
a 24-inch photograph in his possession, taken by Mr. Louis 
M. Rutherfurd, of New York; and to Mr. H. H. Vail, whose 
careful scrutiny of the proof-sheets has been invaluable. 

S. H. P. 

Chicago, June 15, 1869. 

REVISION. 

The progress of astronomical science compels a revision 
of this book. Its scope and methods remain, but care has 
been taken to include all results of established discoveries, 
especially as to solar and planetary physics; and as to the 
dimensions and other data of the solar system, dependent 
on the latest and most trustworthy determinations of the solar 
parallax. 

This work has been aided by the kind criticisms of many 
teachers, and by the careful assistance of my esteemed co- 
laborer, Professor Ira O. Baker, of this University. 

S. II. P. 

Illinois Industrial University, j 
June 15, 1884. \ 



CONTENTS. 



CHAPTER 




PAGE 


I. 


Astronomical Ideas referred to the position of the Ob 






server, . . . . . . 


9 


II. 


Form and Rotation of the Earth, 


15 


III. 


Astronomical Ideas derived from the Motion of the 






Earth, . 


23 


IV. 


The Terrestrial Meridian, ..... 


28 


V. 


Astronomical Instruments, . • , • 


34 


VI. 


Time. Longitude. Right Ascension, 


55 


VII. 


Atmospheric Refraction. Day and Night. Twilight 


65 


VIII. 


Shape of the Earth. Gravitation, 


76 


IX. 


The Distance of the Heavenly Bodies, 


92 


X. 


The Earth's Orbit, 


100 


XI. 


Planetary Motions, ...... 


128 


XII. 


The Sun, ........ 


>5- 


XIII. 


The Moon, 


174 


XIV. 


Eclipses of the Moon, ..... 


193 


XV. 


The Tides, 


203 


XVI. 


The Planets, ....... 


214 


XVII. 


The Minor Planets 


226 


XVIII. 


The Outer Group of Planets, . . . . . 


&3 1 


XIX. 


Comets, ........ 


HI 


XX. 


Meteoric Astronomy, ...... 


*6S 


XXI. 


The Progressive Motion o( Light, 


*7S 


XXII. 


The Fixed Stars 


281 


XXIII. 


The Nebular 1 [ypothesis 


31 1 


XXIV. 


The Constellations 


317 



Vlll 

Appendix, 



CONTENTS, 



328 



TABLES. 

TABLE 

I. Equation of Time, ........ 

II. To find the day of the week on which the first day of 
any month falls, from 1753 to 1905 .... 

III. Elements of the Planets, ....... 

IV. The Minor Planets, 

V. Elements of the Satellites, ...... 



PAGE 

335 

336 
338 
339 
342 



Index, 



343 



PLATES. 



PLATE 

I. The Moon, 
II. Donati's Comet, 

III. Star Clusters, . 

IV. Nebula, . 
V. Nebulae, . 

VI. to XII. Star Maps, 



Frontispiece 

Faces page 263 

» 297 

" 301 

" 3°4 
After page 352 



ELEMENTS 



OF 



ASTRONOMY. 



CHAPTER I. 



ASTRONOMICAL IDEAS REFERRED TO THE POSITION OF THE 
OBSERVER. 



1. The Horizon. — Any person in the open air upon 
level ground, or on the water, finds himself at the center 
of a large circle bounded by the sky. The sky seems to 
be the half of a hollow sphere, or a dome, which rests 
upon the outer edge of the plane on which he stands. 
The line at which the earth and sky appear to meet is 
called the visible, or sensible, horizon. The plane which 
contains this line is the plane of the horizon; any plane 
which is parallel 

to the plane of 
the horizon is a 
horizontal plane. 

2. The hori- 
zon is often hid- 
den by houses, 
forests, or hills, 
while high ob- 
jects, as masts 
or sails of ships, 

towers, or mountain tops, sometimes appear beyond. It" the 




HORIZON 
Fig. 



io ELEMENTS OF ASTRONOMY. 

observer ascends some high place, as a spire or hill, the 
horizon seems to remove as he goes up, and is lower than 
himself. The amount of its depression below a horizontal 
line passing through the observer is the dip of the horizon. 
The angle BAC, Fig. i, measures the dip of the horizon at 
the top of the hill. 

3. Each Observer has his own Horizon. — Strictly 
speaking, the horizon of one person differs from that of any 
other, and each person's horizon accompanies him as he 
goes from place to place. Practically, persons in the same 
vicinity have the same horizon. 

4. The Sky. — The observer is at the center, not only 
of the visible part of the earth's surface, but also of the 
sky which covers it. The sky seems to be a surface at a 
uniform distance, which is immeasurable, or infinite. On 
this surface the sun, moon, and stars seem to move. 

5. Astronomy. — The science which treats of the nature 
and motions of the heavenly bodies is called Astronomy* 
The Law of the Stars. Because these bodies were supposed 
to influence the fortunes of men, a pretended science, 
which assumed to read the stars, and to foretell by them 
future events, was called Astrology, f The Language of the 
Stars. 

6. The real Horizon. — We shall assume that the earth 
is a globe, surrounded by the sky. The center of the sky 
is, therefore, readily understood to be at the center of the 
earth. If a plane pass through the center of the earth 
parallel to the plane of the sensible horizon, and be ex- 
tended every way, the line in which it meets the sky is 



* From aarrjp, aster, a star ; and vojuog, no?nos, a law. Aster is 
allied in dei"ivation to straw and strew; the stars are strewn over 
the sky. 

t From aarrjp, and Aoyoc, logos, a word. 



DEFINITIONS. 
ZENITH 



II 




called the real, or astronomical, horizon. The visible and 
astronomical horizons seem to meet the sky in the- same 
line, because the distance between them is too small to be 
perceived on a surface so far away as the apparent surface 
of the sky. 

DEFINITIONS, 

7. A Sphere is a space bounded by a surface which is 
at every point equally distant from a point within, called 
its center. 

The line in which a plane cuts the surface o\ a sphere 
is the circumference o( a circle (Geom. 744).* When the 



*The ref< 



iierences are 



e to l\.t\ 'n ( ieometrv 



12 



ELEMENTS OE ASTRONOMY. 




Fig. 3- 



cutting plane passes through the center of the sphere, the 
section is a great circle; otherwise, it is a small circle. In 
Astronomy, it is convenient to use the word circle to denote 

what is strictly the 
circumference of a 
circle. 

The Axis of a 

circle of a sphere is 
the diameter of the 
sphere which is per- 
pendicular to the 
plane of the circle 
at its center. The 
poles of the circle are 
the ends of the axis. 
The poles of a great 
circle are equidis- 
tant from every point in the circumference of that circle 
(Geom. 753). 

8. Deductions. — The apparent surface of the sky is 
the surface of a sphere. The real horizon is a great circle, 
and divides the sky into two hemispheres — one visible, 
above, the other invisible, below, the horizon. 

A plumb-line at the observer is found to be always per- 
pendicular to the plane of the horizon. This vertical line, 
prolonged each way, is the axis of the horizon, and the 
points where it would pierce the sky are the poles of the 
horizon. That which is above is called the zenith; that 
which is below, the nadir. 

g. Vertical Circles. — If the observer begin at any 
point on the horizon, and trace a line on the sky directly 
upward, it will pass through the zenith, and thence down 
to the horizon again, to a point opposite to that at which 
he started. He can readily understand that this line pro- 
longed would pass round under the earth, through the nadir, 



CO-ORDINATES. 13 

back to the starting-point, making a complete circle, half 
of which would be visible, and half invisible. 

This circle is a vertical circle, and the plumb, or vertical 
line, is its diameter. 

10. Definitions. — A vertical circle is a great circle of 
the sky, perpendicular to the horizon. The vertical circle 
which passes through the north and south points of the 
horizon is the same as the celestial meridian, which will be 
defined hereafter (32). That which passes through the east 
and west points is called the prime vertical. 

CO-ORDINATES. 

11. A Point. — We state the location of a point by giving 
its direction and distance from some known point or line; 
or, by giving its distance from two points. Thus a desk 
in the school-room may be the third in the fifth row; a 
house is known by its street and number; a town may be 
ten miles north of Boston, or west of Chicago. In each 
case, we state two facts of direction or distance, which are 
called co-ordinates. So we may locate a star by saying that 
we saw it at a certain height, and in a certain direction; 
that is, by giving its altitude and azimuth. 

12. Azimuth. — The azimuth of a star is its angular 
distance from either the north or the south point of the 
horizon to a vertical circle passing through the star. It 
may be measured by any instrument for measuring hori- 
zontal angles. Direct the sights of a surveyor's compass 
toward the north, and then turn the instrument until the 
sights fall on a star; the angle through which they have 
turned will be the bearing, or azimuth, of the star. 

The record of this angle shows its origin, amount, and 
direction; as, N. 20 E., S. 82 12' W., etc. 

The difference between the azimuth and 90 , or the 
complement oi' the azimuth, is called the amplitude. 



14 



ELEMENTS OF ASTRONOMY. 



13. Altitude. — The altitude of a star is its angular dis- 
tance from the horizon, measured on a vertical circle. 
The zenith distance of a star is its distance from the zenith, 



ZENITH 




Fig. 4. 

measured on a vertical circle. It is the complement of 
altitude. These angles may be measured by any instru- 
ment which moves in a vertical plane, as a theodolite, or 
railroad transit. 



14. 



r ECAPITULATION. 



Origin, 

Primary great circle, 
Axis of primary, 
Poles of primary, 
Secondary great circles, 
Principal secondaries, 
Measured on primary, 
Measured on secondaries, 



The position of the observer. 

The horizon. 

The plumb-line. 

The zenith and nadir. 

Vertical circles. 

The meridian and prime vertical. 

Azimuth -j- Amplitude = 90 . 

Altitude -f- Zenith distance = 90° 



CHAPTER II. 

FORM AND ROTATION OF THE EARTH. 

15. The Shape of the Earth. — Several facts prove 
that the earth is round or spherical. 

1. When there is nothing to obstruct or to extend the 
view, the part of the earth's surface seen from any point is 




Mmi QU FROM B ALLOT 
Fig. 5- 



a circle. The circle is made larger by Raising the observer, 
as on a spire, on a mountain, or in a balloon. At ordi- 
nary heights, a person can see no farther on the earth 
with a telescope than without; he only sees more distinctly. 
2. The surface of the sea is curved, as is shown by the 
way in which a ship disappears when it sails from the 
shore. First the hull goes down behind the horizon, then 
the sails, finally the mast heads. If the ship moved on a 

(is) 



1 6 ELEMENTS OF ASTRONOMY. 

flat surface, hull, sails, and masts would all dwindle to a 
point, and vanish together; they would appear again in a 
telescope. 

A monastery, three stories high, stands on the top of Mt. 
Toro, in the center of the island of Minorca, in the Medi- 
terranean Sea. As vessels come toward the island in any 



7// Fig. 6. \ 

direction, the first thing seen by the sailors is the roof of 
the monastery; then the windows of each story in succes- 
sion; then the whole building, as if standing on the sea. 
Presently the mountain appears to rise, and at last the 
island and its coasts are seen. Similar or opposite facts 
are observed whenever a vessel leaves or approaches the 
land. 

3. The world has been circumnavigated by many mar- 
iners from the days of Magellan until now. 

4. The shadow of the earth, as seen in eclipses of the 
moon, is always round. A sphere is the only solid whose 
direct shadow is always round. 

16. The size of the earth.— From the height of a 
mountain and the distance at which its top is visible at sea, 
the size of the earth may be computed approximately. 
Let DBC (Fig. 7) be a great circle of the earth; A, the top of 
a mountain; B, the farthest point on the circle, from which 
the mountain may be seen. Then AB is tangent to the 
circle at B ; AD is a secant, and AC its external segment. 
Therefore, Geom. 333, 

A 7? 2 A 7? 2 

AC: AB :: AB : AD = ^- . \ CD = — AC. 

AC AC 



FORM AND ROTATION OF THE EARTH. 



n 




Example.— Suppose the mountain, 2 miles high, is seen 
at a distance of 126 miles, CD — 7936 miles. 

17. We do not hesitate to say that an orange is round 
although its rind is rough, yet 

its roughness in proportion to 
its size is much greater than 
that of the earth's surface 
where broken by the loftiest 
mountains. If the highest 
peaks of the Andes or the 
Himalayas were accurately 
represented on an 18-inch 
globe, they would project from 
the general surface only about 
.013 of an inch; the thickness 
of a sheet of paper, or of a 
grain of sand. 

18. The apparent revolution of the sky. — The most 
casual observer sees an apparent daily motion of the heavens. 
The sun rises in the east, passes over through the south, and 
sets in the west. At night, the stars rise and set in like 
manner. In the northern sky, the stars seem, to the people 
in our latitude, to move about a fixed point, which is about 
half-way between the horizon and the zenith. Patient watch- 
ing, from hour to hour and from night to night, shows that 
all the stars, in the south as well as in the north, appear to 
move about this point, at greater or less distances. The 
whole circular path of a star is above the horizon, and is 
visible only when the distance of the star from the fixed 
point, that is, the radius of the apparent motion, is less than 
the altitude (13) of the point. 

19. The earth rotates.- The apparent motion of the 
heavens from east to west is caused by the actual rotation 
(A the earth from west to east once in twenty four hours. 
All the appearances are the reverse o\ facts. The sun does 

Ast.— 2. 



1 8 ELEMENTS OF ASTRONOMY. 

not rise, but the horizon sinks below the sun. A star does 
not come to the meridian, but the meridian sweeps by 
the star. 

20. The motion of the earth is not felt, because 
it is uniform, and we move with it. When gliding in a 
boat on a smooth stream we often seem to be at rest, while 
men, trees, and houses pass swiftly by us, yet our reason 
teaches that we move and that the land is still. Persons 
who ascend in a balloon see the ground fall quickly from 
under them, and when they descend the earth seems to 
rise up to meet them. So, though our senses tell us that 
the sun and stars rise and set, it is more reasonable that 
this seeming is caused by the actual rotation of the earth, 
than that the sky, with all the heavenly bodies, immensely 
distant from us, moves about the earth in so short a time. 

21. Galileo. — The doctrine of the rotation of the earth 
was taught by several ancient philosophers. Copernicus 
revived it in 1543, and Galileo believed and taught it in the 
next century. In 1637, at the age of 70, Galileo was forced 
to read and sign a denial of this belief. It is related that 
when he rose from his knees after this abjuration, he struck 
the earth with his foot, and said in an undertone : E pur si 
muove, "and yet it moves," but there is no evidence that he 
was so imprudent. 

DEFINITIONS. 

22. The axis of the earth is the line about which it 
rotates. The points where the axis meets the surface are 
the north and south poles. The direction in which the earth 
turns is east ; that from which it moves is west. 

If a plane pass through the center of the earth perpen- 
dicular to the axis, the line in which it cuts the surface is 
called the equator. The plane of the equator divides the 
earth into two halves, the northern and southern hemispheres. 
Meridians are circles on the surface of the earth which pass 



FOUCAULT'S EXPERIMENT. 19 

through the north and south poles; they are perpendicular 
to the equator and are great circles. 

23. The longitude of a place on the earth is the dis- 
tance of its meridian east or west from an assumed meridian; 
it is measured in degrees on the equator. English astron- 
omers reckon from the meridian of Greenwich observatory; 
French, from the observatory at Paris; American, from 
Washington. The vanity which makes each nation adopt a 
meridian of its own, only creates confusion. Our globes, 
maps, and tables usually refer to the meridian of Green- 
wich, and astronomers are now generally disposed to adopt 
that meridian as the one from which to reckon longitude. 

24. The latitude of a place on the earth is its distance 
north or south from the equator, measured in degrees on a 
meridian. The latitude of the poles is 90 °. Parallels of 
latitude are small circles on the earth's surface, parallel to 
the equator. Places which have the same distance north 
or south of the equator are said to be on the same parallel ; 
those which are on the same line from the equator to the 
poles have the same meridian. 

FO UCA ULT'S EATER I ME NT. 

25. The rotation of the earth made visible. — M. 
Foucault fastened one end of a fine steel wire to the under 
surface of a high ceiling; to the lower end of the wire he 
hung a heavy copper ball, carrying below it a steel pointer. 
This pendulum swung over a place so hollowed out that the 
pointer would move just over the surface; about the edge 
of the hollow was laid a ridge of fine sand, which the pointer 
should pass through at each vibration. That the pendulum 
might not be moved by any other impulse than the simple 
attraction of the earth, he drew it aside from its vertical 
position and tied it by ;i thread; then when it was perfectly 

still, the thread was burned off. and the ball began to oscillate. 



ELEMENTS OF ASTRONOMY. 




As the pointer passed through the ridges of sand, it was seen 
that at each vibration it crossed a little to the right, look- 
ing from the center, of the place where it crossed before. 

26. Theory of 
Foucault's pendu- 
lum. — When the 
pendulum begins to 
swing, being drawn 
only by the earth's at- 
traction, it must move 
in the plane which con- 
tains the three points, 
the point of suspension, 
the point from which it 
started, and the center 
of the earth. It can 
not of itself leave this 
plane of vibration, and 
there is no force with- 
out to cause it to turn 
aside; it must go on 
therein to the end 
of the vibration. The 
next vibration begins 
in the same 
plane, and, 
therefore, like 
the first, ends 
in it, and so 
each subse- 
quent vibra- 
tion. That to 
which the pendulum is suspended has, of course, the motion 
of the earth at the place where the experiment is performed; 
but, as the wire is so fastened that no rotary or twisting 
motion can be communicated to it, the forward motion of 




Fig. 8. 



FOUCAULT'S EXPERIMENT. 



21 




Fig. 9. 



the point of suspension only carries the plane of vibration 

forward, without twisting it to the right or left. 
The ball, then, does 

not move toward the 

right; its apparent mo- 
tion makes visible the 

actual motion of the 

earth beneath it, toward 

the left, that is, toward 

the east. To view this 

experiment rightly, the 

observer should be at the 

center of the circle; as 

this is not possible, he 

should look across the 

center to the opposite 

side; then wherever he 

may stand, the ball will seem to move to the right, while the 

earth beneath moves toward the left. 

27. At the pole 
(Fig. 9), the point of sus- 
pension does not move ; 
the plane of vibration 
is fixed, and the earth 
rotates beneath. 

At the equator (Fig. 1 o), 
the meridians being per- 
pendicular to the equator 
are parallel to each other, 
and heme have always 
the same position re la 
live to the plane o\ vi- 
Fi e- l * bration. 

Between ///<• equator 

and tlii- pole (Fig. 11), the meridians converge, or. what 

amounts to the same, the new positions which each meridian 




22 



ELEMENTS OF ASTRONOMY. 



takes as the earth rotates, make with the old, angles which 
constantly increase. Hence, as the pendulum maintains its 

position, although it may 
have been started in the 
plane of one of these me- 
ridians, an angle is soon 
formed between them 
which constantly in- 
creases until they again 
coincide. At the poles, 
they coincide at the end 
of 24 hours; between 
the poles and the equa- 
tor, the time gradually 
increases, and at the 
equator it is infinite. 

28. The Gyroscope, 

when rotating in a vertical plane, remains always in that 
plane. M. Foucault used this instrument, watching its 
turning with a telescope, with the same results, explained 
by the same theory. 




Fig. 11. 



29. 



RECAPITULATION. 



Origin, 

Primary great circle, 
Axis of primary, 
Poles of primary, 
Secondary great circles, 
Measured on primary, 
Measured on secondaries, 



The rotation of the earth. 

The equator. 

The axis of rotation. 

The north and south poles. 

Meridians. 

Longitude, terrestrial, to 180 . 

Latitude, terrestrial, to 90 . 



CHAPTER III. 

ASTRONOMICAL IDEAS DERIVED FROM THE MOTION OF THE 
EARTH. 

30. Axis of the heavens. — The axis of the earth, ex- 
tended in each direction until it meets the sky, becomes the 
axis of the heavens, or the line about which the sky seems to 
revolve. The points where this line meets the sky are the 
north and south poles of the heavens. 

31. Equinoctial. — If the plane of the equator is ex- 
tended every way, the line in which it meets the sky is a 
great circle, called the celestial equator, or equinoctial. 
The stars appear to describe circles about the poles of the 
heavens, parallel to the equinoctial; the circles may be called 
circles of daily motion. 

32. Meridians are great circles on the sky, perpen- 
dicular to the equinoctial, and passing through its poles. 
Celestial meridians must be imagined on the sky, as terres- 
trial meridians are imagined on the surface o( the earth. 
As every place on the earth has its own meridian passing 
through the north and south poles, so each star in the 
heavens has its meridian passing through the poles o( the 
heavens. When we speak of The Meridian, as when we 
say the sun, or a star, comes to, or passes the meridian, we 
refer to the plane o( the terrestrial meridian o\ the place 
where the observation is made. 

(13) 



2 4 



ELEMENTS OF ASTRONOMY. 



CO-ORDINATES. 

33. Declination. — The distance of a heavenly body 
from the equinoctial, measured on a meridian, is called its 
declination. Declination corresponds to terrestrial latitude; it 
is north or south declination as the object is north or south 
of the equinoctial. The declination of the poles is 90 . 



ZENITH 



HfOLl 



OFSK) 



^%> 



aV^fe 




NADIR 
Fig. 12. 



34. Polar distance. — The polar distance of a star is its 
distance from the nearest pole, measured on a meridian. 
Declination -{- polar distance always equal 90 °. 



CO- OR DIN A TES. 2 5 

35. Right ascension corresponds most nearly to ter- 
restrial longitude. It is measured on the equinoctial, east- 
ward from a fixed point, to the meridian of the celestial 
body. Right ascension is measured from a point called the 
vernal equinox, or first point in Aries, which is indicated by 
the sign °f. The meaning of these terms will be explained 
hereafter. (55.) 

36. The place of a star. — We locate a place on the 
earth by giving its latitude and longitude; we locate a star 
on the sky by giving its declination and right ascension; we 
tell where it seems to be at any moment when it is above 
our horizon by giving its altitude and azimuth. We refer 

Latitude and longitude, terrestrial, to the Equator ; 

Declination and right ascension to the Equinoctial; 

Altitude and azimuth to the Horizon. 
The declination and right ascension of a star are the same 
for observers at all places on the earth; the altitude and 
azimuth vary with the position of the observer. 

37. The sky as seen from the pole. — Let us sup- 
pose that a person is at the north pole, and that during the 
long night there, he sits in the same position for twenty-four 
hours. The earth rotates, and he turns with it. He is not 
conscious of motion, and therefore the stars seem to pass 
before him ; they go toward his right hand, pass behind him, 
and re-appear upon his left. The pole of the heavens is 
over his head, in the zenith (8). His real horizon (6) coin- 
cides with the equinoctial. All heavenly bodies which have 
north declination, are above the horizon and are visible; all 
which have south declination are invisible. Celestial me- 
ridians coincide with vertical circles (9); the altitude (13) of 
a star is the same as its declination. The cardinal points can 
not be distinguished, for north is over his head: south is 
under his feet; westward is always toward his right hand, and 
eastward toward his left. Whatever route he lakes is toward 
the south, that is, away from the north pole. 



26 ELEMENTS OF ASTRONOMY. 

38. The sky as seen from the equator. — An ob- 
server at the equator will find the poles of the sky in his 
horizon. The equinoctial will pass through his zenith, and 
will coincide with the prime vertical (10). The sun and 
stars near the equinoctial will rise directly in the east ; and 
will set directly in the west ; other stars will seem to describe 
smaller circles whose planes are perpendicular to the horizon, 
and each star will be visible just twelve hours. 



THE LATITUDE OF THE OBSERVER. 

39. The latitude of the observer is equal to the 
altitude of the pole. — When the observer -is at the equa- 
tor, his horizon extends to the poles of the sky. If he goes 
ten degrees north of the equator, his zenith will be ten 
degrees north of the equinoctial, and his horizon will be 
removed ten degrees beyond the north pole; the pole will 
seem to have risen ten degrees above his horizon. At 20 
north latitude the altitude of the pole will be 20 . At the 
pole, latitude 90 (24), the pole of the heavens will be in 
altitude 90 °, or in the zenith (37). 

Hence, the latitude of a place may be found by finding the 
altitude of the nearest pole. 

40. The length of a degree of latitude.— We shall 
have gone one degree to the north whenever we shall have 
increased the altitude of the north pole one degree. The 
length of a degree of latitude differs slightly at different dis- 
tances from the equator, being shortest near the equator, 
longest near the pole. The average is about 69% miles. 

Multiplying the length of a degree by the number of de- 
grees in a circle, we find the circumference of the earth to 
be 24,930 miles; this gives a diameter of 7936 miles nearly, 
as found before (16). 

41. The pole star. — The north pole of the heavens is 
near a rather bright star, called the North Star, Polaris, or 



THE LATITUDE OE THE OBSERVER. 27 

the Pole Star. To the ordinary observer the pole star seems 
stationary, yet careful observation shows that it has a daily 
motion about the pole, like other stars in the sky. The 
sailor on the ocean, the Arab in the desert, the Indian in the 
forest, each considers this the only motionless star in the 
heavens, and guides himself by it. 

No similar star shows so nearly the place of the south 
pole of the heavens. 

42. Circle of perpetual apparition. — The largest 
circle about the pole, which does not pass below the horizon, 
is called the circle of perpetual apparition. The stars within 
it do not set, and vanish only because of the superior light 
of day. A similar circle about the opposite pole, which does 
not come above the horizon, is the circle of perpetual occupa- 
tion. The stars within this circle never rise. The radii of 
the circles of perpetual apparition and occultation are equal 
to each other, to the altitude of the pole, and (39) to the 
latitude of the place of observation. (See Fig. 12.) 

43. To a person south of the equator the circle of per- 
petual apparition is about the south pole; to one at either 
pole both circles coincide with the horizon and the equi- 
noctial; to one at the equator, they are nothing. 

The heavenly bodies within the circle of perpetual ap- 
parition are called circumpolar bodies. 



44. RECAPITULATION. 

Origin, The apparent daily motion of the 

sky caused by the actual daily 
rotation of the earth. 

Axis, The earth's axis prolonged. 

Poles of primary, North ami south poles o\ the sky. 

Primary great circle. The equinoctial. 

Secondary great circles. The celestial meridians. 

Measured on primary, Right ascension, to l6o°, 

Measured on secondaries, Declination • Polar Dis. oo°. 



CHAPTER IV. 



THE TERRESTRIAL MERIDIAN. 



45. The plane of the meridian. — A terrestrial me- 
ridian has been denned (22) as a circle of the earth which 
passes through the north and south poles. A line on 
the floor, a fence, or the founda- 
/ tion of a building, when placed 

precisely north and south, will mark 
a meridian line, and the posts of the 
fence, or the side of the building, 
if placed truly plumb, will be in the 
plane of the meridian. 

46. Hang a plummet by a fine 
strong line, so that the weight may 
dip into a vessel of water; this will 
prevent the line from swinging by 
the force of the wind. Fix a second 
line due north of the first, and the 
two lines will indicate the plane of 
the meridian quite accurately. While 
the eye is at one line, any object on 
the earth or the sky seen to pass the 

other line may be said to cross the meridian. 

As these lines can not be seen in the night, a still simpler 

way is to fix some stand-point fifty or one hundred feet north 

or south of a corner of a building, which is usually plumb. 

A star passes the meridian at the instant when an observer, 

standing at this point, sees it disappear behind the house. 
(28) 




Fig- 13- 



THE MEASURE OF A YEAR. 



29 



47. Culminations. 

— The passage of a star 
across the meridian is 
called its culmination. 
As the plane of the 
meridian extends infi- 
nitely in both directions 
through the axis of the 
sky, each star passes the 
meridian twice in trav- 
ersing its curve of daily 
motion; once above, 
and once below the 
axis. The upper pas- 
sage is called the supe- 
rior, the lower, the infe- 
rior, culmination. The 
inferior culmination is 

visible when the star is within the circle of perpetual appari- 
tion (42). 

THE MEASURE OF A YEAR. 




Fig. 14. 



48. The same stars pass the meridian at differ- 
ent hours of different nights. — When the plane of the 
meridian has been found (46), let us watch the culmination 
of some star, and let us note the time; suppose it to be 
eight o'clock in the evening. The culmination of the same 
star on the next night will occur about four minutes earlier 
than it did the night before, and so on for the following 
nights. Patient watching shows that the same star will noi 
come to the meridian again at the same hour until the end 
of a year. 

On any day of the year certain stars will culminate at 
about midnight; ami on every return o( that day these stars 
will again culminate at the same hour. On no other day 



3° 



ELEMENTS OF ASTRONOMY. 



of the year will they come to the meridian, except for 
inferior culmination, at midnight. 

49. The index of a year is thus found quite nearly. 
It is the time which passes from the culmination of a certain 
star at a certain hour, until the next similar culmination 
of the same star at the same hour. 

50. Observations of the sun at noon. — When the 

sun crosses the meridian, we say it is noon. Let us measure 
the shadow which an upright post casts at noon upon a level 
surface at its base. From the length of the shadow and the 
height of the post, we may find by a circular protractor, or 
by computation, the angle of elevation of the sun, or its 
altitude (13). The shadow cast by a window-sill upon the 
floor will answer the same purpose. 

51. From the 20th of March to the 22d of Sep- 
tember. — On the 20th of March we shall find the altitude 




20 J UN. 



Fig. 15. 



of the sun equal to the difference between the latitude of the 
place and 90 , called the co-latitude of the place; but as the 
meridian altitude of the equinoctial is equal to the same 
quantity (App. I), we see that the sun must be on the equi- 
noctial; its declination is nothing (33). On the next day 
the shadow of the post at noon will be shorter. Thus, day. 
by day, the shadow diminishes until the 20th of June; then 



THE SUN'S PATH. 3 1 

the angle is 23^° more than the co-latitude of the place, 
and the sun's declination is 23^° north. After the 20th 
of June the shadow increases, and the sun approaches the 
equinoctial, crossing it again on the 2 2d of September. 

52. From the 22d of September, the shadow con- 
tinues to increase, and the angle to diminish, until the 2 2d 
of December. Then the altitude of the sun is 23^° less than 
the co-latitude of the place, and the declination of the sun 
is 23^° south. 

53. Example. — When the observer is in lat. 40 , the 
co-latitude of the place is 50 . 

By observation we find, on 
March 20, Sun's altitude, 50 ; . \ Sun's declination, o°. 
June 20, " " 73^; " " 23^ N. 

Sept. 22, " " 50; " " o. 

Dec. 22, " " 26%) " " 23% S. 



THE SUN'S PATH. 

54. From these observations we learn : 

1. That the sun crosses the meridian at different altitudes, 
varying regularly during the different seasons of the year. 

2. That the sun passes the meridian at the same altitudes 
at regular intervals of a year. 

3. That the sun moves alternately 23^° north, and 23 l _. ° 
south of the equinoctial, once each year. 

55. Equinoxes. — As the horizon (8) and the equinoctial 

(31) are both great circles, they divide each other into two 
semicircles (Geom. 748). Therefore, when the sun is on 
the equinoctial, it is as many hours above as below the 
horizon, and the day is equal to the night. Hence, the 
points where the sun in his annual motion crosses the 



3 2 



ELEMENTS OF ASTRONOMY. 



equinoctial are called equinoxes* That which the sun passes 
in March, going from south to north, is the vernal equinox ; 
that passed in September, from north to south, is the 



NORTH POLE OF SKY. 




'SOUTH POLE OF SKY 
Fig. 16. 

autumnal equinox. The vernal equinox is the point from 
which right ascension is measured (35). 

56. Solstices. — The sun, having gone farthest from the 
equinoctial, remains at about the same distance for several 
days, and then seems to turn and go back again. The 



* ALquns, equal ; nox, night. 



THE SUN'S PATH. 33 

points where the sun's declination is greatest, are called the 
solstices, or solstitial points* because the sun seems to pause 
there awhile and then return to the equinoctial. The sun 
comes to the summer solstice on the 20th of June; to the 
winter solstice .on the 2 2d of December. The solstices are 
90 from the equinoxes. 

57. Colures. — The celestial meridian which passes 
through the equinoxes is called the equinoctial colure ; that 
which passes through the solstices is called the solstitial 
colure. 

58. The ecliptic. — The path which the sun seems to 
follow in the sky is called the ecliptic. It is a great circle, 
and its plane makes an angle with the plane of the equi- 
noctial of about 23^°. 

The angle is exactly 23 ° 27' 13". 51 (Jan. 1, 1884). 

59. The measure of a year is determined by the apparent 
motions of a fixed star (49). With a very slight difference, 
the same time elapses between two successive passages of the 
sun over a definite point, as an equinox, or a solstice. 



60. RECAPITULATION. 

The plane of the meridian may be shown practically by plumb- 
lines, or by the vertical walls of a building. 

A star culminates when it seems to pass the meridian. 

A year elapses between two successive culminations ^ the same 
star at the same time of night. 

A year elapses between two similar culminations of the sun. 

Equinoxes. The points where the sun crosses the equinoctial. 

Solstices. Points at which the sun is farthest from the equinoctial. 



* So/, the sun; stare, to stand. 



CHAPTER V. 



ASTRONOMICAL INSTRUMENTS. 



61. The development of the science of Astronomy has 
depended largely upon the improvement in astronomical 
instruments. These are in general, 

Telescopes, to see distant objects. 

Graduated circles, to measure angles. 
Accurate clocks, to measure time. 



THE TELESCOPE. 



62. Refraction. — A ray of light which passes obliquely 

from one medium into 
another of different den- 
sity, as from air to glass, 
or from water to air, is 
turned or bent from its 
course. This bending is 
called refraction. Pass- 
ing into a denser medium, 
the course of the ray is 
more nearly perpendic- 
a rarer medium, its path is farther 
A ray which is perpendicular to 




Fig. 17. 

ular to the surface; into 
from the perpendicular. 



the surface of the new medium is not refracted. 
(34) 



THE VISUAL ANGLE. 



35 



The ray AB, which passes into the glass prism, is turned 
toward the perpendicular BG, and goes on to the point D. 
There it is again refracted, but as it passes into a rarer 
medium, it is turned from the perpendicular, into the line 
DE. The object A, from which the ray comes, appears to 
be at A, in the line ED. 




w 



Fig. 18. 



63. A Lens is a transparent substance, usually glass, 
whose opposite surfaces are both 
curved, or one is curved and the 
other is plane. Sections of dif- 
ferent forms are shown in Fig. 
18; a, plano-convex; b, double- 
convex; c, plano-concave; d, 
double-concave; e, meniscus. 

The curved surface is usually 
part of the surface of a sphere. 

The line which passes through the center of the lens perpen- 
dicular to the opposite surfaces is its 
axis. 

The lens may be considered as 
made of a great number of prisms 
arranged symmetrically about the 
axis. Rays which pass through a 
convex lens are bent toward the 
axis. Parallel rays are made to meet 
Fig. 19. in the axis at a point called the focus. 

The distance of this point from the 
center of the lens is the focal distance. 



CENTER 

OF < 

SPHERE 



THE VISUAL ANGLE. 



64. An object which subtends a large angle at the eye is 
either large or near ; one which subtends a small angle is 
small or distant. The arrows 1 and 4, subtend a large 



36 



ELEMENTS OE ASTRONOMY. 




Fig. 20. 

angle, while the small arrow 3, and the distant arrow 2, 
subtend a small angle. The angle at the eye is called the 
visual angle. 

65. Effect of convex lenses. — A convex lens increases 
the apparent size of an object seen through it, by increasing 
its visual angle. The arrow 1 , seen without a lens appears 
no larger than the small arrow at 3, included between the 
lines a and b ; but seen through the lens, the rays c and d 
from the ends of the arrow are so refracted as to enter 




Fig. 21. 



the eye, and the object has the apparent size of the larger 
arrow at 2. 

Another lens between the first and the eye refracts these 
rays again, makes the visual angle still larger, and magnifies 
the object still more. Several lenses, properly arranged, 
form the essential part of a microscope. 

66. Refracted image. — All the rays which pass from 
one point of an object through the lens, are brought together 



THE VISUAL ANGLE. 



37 



in a second point at a certain distance, making an image of 
the first. The same is true of the rays from any other point, 
and thus every point of the object is represented in an image 
on the opposite side of the lens. This image may be re- 
ceived on a screen of ground glass, as in a photographer's 
camera. 

67. Illustration. — In the diagram, all the rays which 
pass through the lens from the point of the arrow are 




Fig. 22. 



united on the screen in the point of the image; all the rays 
from the tip of the feather are united on the screen in an 
image of the feather. Were it not for confusion we might 
draw a series of rays from any other point of the arrow, and 
find them unite in a point of the image. If the screen is 
moved a little nearer the lens, or a little farther away, the 
rays which pass through the lens from the same point o\ the 
object, are not gathered into a single point, but are scattered 
over a small surface, giving a multitude o\ obscure and inter- 
fering images, as at a. 



38 



ELEMENTS OF ASTRONOMY. 



REFRA C TING TELESCOPES. 

68. A refracting telescope is a tube containing at one 
end a large lens, called the object-glass, which gathers a great 
number of rays from the object viewed and condenses them 
to form an image, and one or more smaller lenses near the 
other end, which form an eye-piece, or microscope, to magnify 
this image. 

69. A large object-glass increases the intensity of the 
light at the image. When a microscope magnifies any 
number of times, as ten, the light which comes from the 




object is distributed over ten times the original surface, and 
the brightness or intensity of the light on any portion is only 
one tenth as great. Hence we may magnify an object so 
much, and make its light so feeble, that its form can not be 
distinctly seen • it fades away as in the twilight. If we would 
use a higher magnifying power we must find some way to 
increase the light; in the telescope this is done by enlarging 
the object-glass. 

70. Example. — The area of the object-glass of the Chi- 
cago refractor, is to that of the Cambridge instrument as 31 
is to 25. If the two lenses are precisely equal in other 
respects, the light will be in the same ratio ; if one telescope 
will admit a magnifying power of 2500, the other can use a 
magnifying power of 3100. 

71. Power of telescope. — Different eye-pieces of vari- 
ous powers may be used with the same object-glass, changing 
for the time the power of the instrument ; the limit of power 



REFLECTION 



39 



being fixed by the amount of light furnished by the object- 
glass. A good lens is highly transparent, of uniform density 
that it may have uniform refractive power, and quite free 
from bubbles or scratches. Its size is therefore practically 
limited by the great difficulty of casting glass in large masses 
suitable for astronomical purposes. 



REFLECTION. 



^ANCLE OF INCIDENCE 
ANCLE OF REFLECTION 



Fig. 24. 



72. A ray of light which meets a plane mirror is turned 
back, or reflected, and passes away 

from the reflecting surface, making 
the angle of reflection equal to the 
angle of incidence. 

73. A concave mirror may be 

considered as composed of a great 
number of plane mirrors arranged 
about a hollow spherical surface. The 
point where parallel rays meet after 
reflection is called the focus. 

74. Reflected image, — At a 
certain distance, all the rays of 
light which come from one point 
of the object viewed, to various 
parts of the mirror, are, by reflec 
tion, again brought together, and 
form the reflected image o( the 
point. In a similar way, an image 
of the entire object is formed, and 
may be received on a screen, as in 
the ease o( a convex lens (66). 

75. Place of the image. — The image made by a lens 
is on the side opposite the object ; that made In a mirror 
is on the same side as the object, We look through the 




Fig. 25. 



4 o 



ELEMENTS OF ASTRONOMY. 




IMAGE 



OBJECT 



Fig. 26. 



lens, toward the object. When using the mirror, we turn 
away from the object and see an image of it made by the 
reflecting surface. 



REFLECTING TELESCOPES. 



76. A reflecting telescope is a tube having at one end 
a concave mirror, called a speculum, which .gathers the rays 
of light from the object viewed into an image; the image 
is magnified by a set of lenses in an eye-piece. The 
speculum of a reflector evidently serves the same purpose 
as the object-glass of a refractor; each furnishes a brilliant 
image for the magnifying power of the eye-piece. 

77. Newton placed before the speculum a small plane 
mirror which reflected the rays a second time and turned 
them into an eye-piece in the side of the tube (Fig. 27). 
Gregory used a small concave mirror which returned the 
rays through a small hole at the center of the speculum 
(Fig. 28). Herschel, by inclining the speculum slightly, 
threw the reflected rays directly into the eye-piece fixed 
obliquely at the mouth of the tube (Fig. 29). 

78. The speculum is usually made of some alloy which 
will take a high polish, and will not tarnish readily. 

Silver-on-glass specula have lately been made of good 
quality and at reduced cost. The concave surface of a 
block of glass is accurately ground and polished ;. it is then 



REFLECTING TELESCOPES. 



41 



coated with a film of silver, chemically deposited, on which 
an excellent reflecting surface is procured. 




Fig. 27. 



Fig. 28. 




.... ..... 



"■-•" ■ : ' ' ^_ "■ "■" "" ': : ....... — 



Fig. 29. 



The largest refractor yet made is at Pulkova, Russia, 30 



inch 



es in aperature. 



42 



ELEMENTS OF ASTRONOMY. 




pig, 30.— Lord Rosse's 6 ft. Reflector. 

The largest reflectors are those of Sir William Herschel 
and of Lord Rosse. The speculum of Lord Rosse's telescope 
is six feet in diameter. 



MEASURING INSTRUMENTS. 

79. The line of collimation. — If measurement is to 
be assisted by a telescope, we must know when the instru- 




M ATI ON 



EYE PIECE 



OBJECT GLASS 



merit is pointed precisely at the object whose position is to 
be found. It is not enough to say that a point is near the 



THE TRANSIT INSTK UMENT. 



43 




center of the visible field. The line which joins the centers 

of the object-glass and eye-piece of a telescope is called its 

line of collimation, or its axis. The 

telescope is so placed that one end 

of this line enters the eye and the 

other touches the precise point 

which we observe. a$ 

80. The reticule. — The axis 
is marked by two fine wires, one 
vertical, the other horizontal, which 
cross in the focus of the object- 
glass. In some telescopes more 

wires are used, but in any case the system is called a reticule, 
or net-work. The lines, though called wires, must be the 
finest possible, and are usually of spider's web. They are 
fastened to a ring, A, which is adjusted in the tube of the 
telescope by the screws, <?, a. In the day, they are seen as 
two fine dark lines across the object viewed. In the night, 
they must be lighted by a lamp placed where its rays may 
fall on the reticule without coming directly to the eye of the 
observer. They then appear to be two bright lines against 
the dark background of the sky. 



Fig. 32. 



THE TRA NSI T INS 1'R I 'MEN l\ 



81. The passage of a star across the meridian has boon 
called its culmination (47); it is also called a transit, and a 
telescope fitted to observe this passage is a transit instrument, 
whose line of collimation must always be in the plane o\ the 
meridian, and whose only motion must be on a pivot, at 
right angles to that plane. The ends o( the pivot must rest 
upon a firm support, usually o( solid masonry. The fine 
lines of the reticule take the place o\ the comer oi the barn. 
or the plumb-lines oi (46), and the observer's sight is assisted 
by the power oi his telescope, 



44 



ELEMENTS OF ASTRONOMY. 




Fig. 33- 



The figure must be understood to show only the essential 
parts of the instrument, stripped of all adjuncts or con- 
veniences. 

82. The use of the Chronograph in observing a 
transit. — A sheet of paper is wrapped about a cylinder 
which is made to revolve at a uniform rate under a pen; the 
pen draws a continuous line upon the paper. It is held near 
an electro-magnet, and when the magnet acts the pen is 
moved slightly aside for an instant, causing a notch in the 
line. The pendulum of an astronomical clock is so con- 
nected with the magnet that a notch is made at each second's 
beat. The whole apparatus is called a chronograph.* 



* Kpovo-, chronos, time ; ypafetv, 
chronograph, a time marker. 



graphein, to write or mark 



THE TRANSIT INSTRUMENT. 



45 



The observer at the telescope has at his hand a key, and 
when he presses it the pen of the chronograph 
will make a notch in the line. While he 
watches a star the clock pendulum is noting 
seconds. When the star is seen to approach 
the vertical line of the telescope the observer 
taps his key quickly several times; then at the 
instant when the star seems to be on the wire, 
another tap causes a notch to be made, and its 
place in the line between two made by the 
clock, shows the time of the transit. 

This method of observation, invented by 
Prof. O. M. Mitchel, and known as the 
American method, is now used in all observa- 
tories. 



The lines of Fig. 34 are the record of an 
astronomical clock unwound from a chron- 
ograph; the hour and minute being marked at 
the end of the line, and the seconds by the 
notches. The notches AB show the approach 
of a star; the transit is marked by the notch C. 
If the space from C to 7 is 0.35 of the space 
7 to 8, then the record shows that a transit 
was observed at the first 
wire at 7 h. 16 m. 7.35 
sec. 

83. Additional 
wires. — To insure still 
greater accuracy, addi- 
Fig< gg, tional wives are placed 

Oil each side of the 
central wire, and the time is noted as the star 
passes each in succession. The average or 
mean of the observations is taken as the time 
Of the transit, thus : 




>/JS 



M4* 



?tf s 



\\\ 



> >iO s 



6 s 

P 5 9 

s 
>/* 

,0* 



P>8- 34. 



46 ELEMENTS OF ASTRONOMY. 

Transit over ist wire, n h. 10 m. 44.25 sec. 
" " 2d " " " 45.10 " 

tt 3d it it it 4 - g6 tt 

" 4th " " " 46.82 " 

" 5th " " " 47.66 ". 

Mean time of transit, 11 h. 10 m. 45.958 sec. 

84. Altitudes. — By the vertical wire, we may find the 
instant of the transit of a star; by the horizontal wire, we 
get its altitude. To measure the altitude, we either fasten a 
graduated circle to the telescope, and observe what portion 
of its circumference passes a fixed point as the telescope is 
moved up or down, or we make the instrument move beside 
a fixed circle, and so observe the arc passed. The telescope, 
like that of the transit instrument, must move in the plane 
of the meridian, upon a pivot which lies due east and west, 
and rests firmly on solid masonry. 



THE MURAL CIRCLE. 

85. The mural circle is a circle of metal, which, as 
it turns on its pivot, keeps the telescope attached always in 
the meridian; the circle is accurately graduated upon its rim. 
When the telescope is exactly horizontal, a stationary index 
should point to zero on the circle; as the telescope is moved 
from that position, a portion of the rim passes by the index, 
which thus shows the amount of elevation. If the work- 
manship of the instrument were absolutely perfect, and it 
could be made so firm as to resist change of form in the 
slightest degree for any cause, all parts of the rim would 
indicate the same amount of motion ; but since perfection 
can neither be attained nor kept, several indexes are placed 
at equal distances about the circle, and the average of their 
readings is taken. The indexes are microscopes, furnished, 
like the telescope, with spider-lines (80). 



THE MURAL CIRCLE. 



47 



86. The mural circle in the National Observatory at 
Washington is five feet in diameter; it carries on its edge 
a band of gold, divided into spaces of 5' each; it is read 




Fig. 36. 



by six microscopes, which detect a motion of a single 
second. 

87. A micrometer is a contrivance for measuring very 
small spaces. Two parallel spider-lines arc so arranged in 
the focus of a microscope that the space between them 
may be increased or diminished by turning a screw. If the 
screw has ten threads to the inch, one turn of the screw 
moves the movable wire one tenth o( an inch. 1 el the head 



4 8 



ELEMENTS OF ASTRONOMY. 



of the screw be made so large that its rim may contain one 
hundred easily observed parts, and note how many of these 



\j 






\J 



r\ 



Fig. 37- 



divisions pass a fixed index. 



Each space marks y^- of a 



turn, or 



of an inch, in the motion of the wire. 



88. To measure seconds. — In the reading microscopes 
mentioned before (86), five turns of the screw cover one 
space on the graduated circle, or five minutes. One turn 
of the screw gives one minute, and as the head of the screw 
has sixty divisions, each division indicates one second of arc. 

The mural circle may do the work of a transit instru- 
ment if furnished with a suitable web of vertical wires. 

The transit instrument is sometimes placed in the prime 
vertical, instead of in the meridian. 

89. To find the horizontal position of the tele- 
scope. — While readings are made so accurately, it is 
evidently very important that the starting-point should be as 
carefully found. The surface of a liquid at rest is horizontal ; 
a trough containing mercury is placed where the telescope 
of the mural circle may point directly upon its level surface. 
The telescope is first pointed to a star, and the readings of 
the circle are noted; then the glass is turned to the image 
of the same star reflected from the mercury. The lines from 
the distant star, S£> and S'O, are parallel, and make equal 
angles with horizontal lines through D and O (Geom. 138); 



THE MURAL CIRCLE. 



49 




Fig. 38. 



the lines S'O and OD make angles of incidence and reflec- 
tion at 0, which are equal (72); the line DO makes angles 
with the horizontal 
lines through D and 
which are equal 

(Geom. 125); there- / 

fore the image of the 
star seen in the line 
DO is seen as far 
below the horizon as 
the star itself, on the 
line D S, appears 
above. The readings 
of the circle are again 
taken, and the true 
horizontal line of the 
instrument is midway 
between the two. A 
correction is to be 
made for refraction, which will be explained hereafter (124). 

90. The meridian circle. — The mural circle has been 
chosen for explanation because of its simple form. In all 
modern observatories the mural circle has been displaced by 
the more complex instrument, called the meridian circle. 
This is essentially a transit instrument, provided with care 
fully graduated circles, microscopes for reading, apparatus for 
inverting, and other conveniences, all o\ the most accurate 
workmanship. 

In the example presented, we note, first, two substantial 
iron piers, on which the pivots of the telescope rest. Be 
tween the piers the axis carries on either side ot the 
telescope a circle, graduated en its side. There is 0110 

microscope for reading the circle on the left, four tor that 
on the right. Each microscope en the right has a micro 
meter near its outer end tor minute reading. The micro 
scopes are carried by the cylinders seen above the picas, and 

Asl.— 4. 



5° 



ELEMENTS OF ASTRONOMY. 




Fig. 39.— Meridian Circle. 



may be moved to read different parts of the circles. The 
bar over the telescope carries the striding level It may be 
lifted by the handles, reversed to show that the axis is level, 
or laid aside. 



ALTITUDE AND AZIMUTH INSTRUMENT. 



51 



ALTITUDE AND AZIMUTH INSTRUMENT. 

91. The mural or meridian circle always points to one 
vertical circle of the sky; it observes a star only when it 




Fig. 40.— A Theodolit* 



comes to that vertical. Let us now suppose that the pivot 
of the telescope is fixed, not upon immovable supports, but 
to a post which may turn upon its own vertical axis, ami 
let this post stand on a horizontal circle having the same 
moans for careful reading which have been described for 
circles in a vertical position. The telescope may now lv 



ELEMENTS OF ASTRONOMY. 




Fig. 41. — Railroad Transit. 



turned to any star; the 
vertical circle of the 
instrument shows the 
altitude of the star on 
a vertical circle of the 
sky, while the horizon- 
tal circle shows the 
bearing, or azimuth 

(12). 

The common transit 
of the railroad en- 
gineer, when fitted 
with a vertical circle, 
is an altitude and azi- 
muth instrument. The 
vertical circle takes 
elevations; the hori- 
zontal, bearings. 



THE EQUATORIAL. 



92. The telescope mounted equatorially. — When a 

star has been made to appear in the field of a telescope, it 
soon passes out of sight, because the earth moves the instru- 
ment past the star. If the observer desires a longer view 
of the object he must follow it with the telescope. His 
attention is distracted by constant efforts to keep the star in 
view, and the difficulty increases with the magnifying power 
of the instrument. It is overcome by a system of machinery 
for moving the telescope, called an equatorial mounting. 

The principal pivot is placed parallel to the axis of the 
sky; it rests on the sloping face of a solid pier, a block 
of stone, or a heavy frame-work of iron. This pivot is moved 
by clock-work, and turns the telescope westward as fast as 
the earth turns eastward, thus counteracting the motion of the 



THE EQUATORIAL. 



53 



earth. But this would allow the telescope to move only 
on the great circle of the sky which is at right angles to the 
axis of the sky — the equinoctial. A second pivot, at right 
angles to the first, 
allows the tube to 
be turned north or 
south of the equi- 
noctial. The in- 
strument is turned 
to a star, the sec- 
ondary pivot is 
clamped fast, and 
the machinery 
turns the first pivot 
with a motion equal 
to that of the earth, 
and in the opposite 
direction. 

Powerful refrac- 
tors are usually 
mounted equatori- 
ally, since they are 
used chiefly for 
studying the phys- 
ical appearances of 
the heavenly bod- 
ies, and must com- 
mand the entire 
sky. 

93. As mural and 
meridian circles 
and transit instru- 
ments do not move out of a fixed plane, they require only .1 
narrow opening through which the stars may be seen. 
Kquatorials are usually covered by a large hemispherical 
or cylindrical dome which has an opening at one side from 




Fig. 42- 



54 ELEMENTS OF ASTRONOMY. 

the base to the top. The dome rests on rollers, and wheel- 
work turns it to present the window to any quarter of the 
heavens. 

The instruments described are by no means all that may 
be found in large and well-appointed observatories. They 
include, however, the most important, and others differ in 
detail rather than in principle. 



94. RECAPITULATION. 

A telescope contains a large lens or a mirror, which furnishes an 
intensely bright image of a distant object, to be magnified by one or 
more lenses in the eye-piece. 

The wires of the reticule determine the precise point observed. 

For measuring angles, the telescope is attached to a graduated 
circle, either vertical, or horizontal, or to both. 

Observations of angles are made more accurate by the micrometer; 
of time, by connection with a chronograph. 

The transit instrument observes the instant at which an object in 
the sky passes the meridian. 

The mural circle gives the altitude of such a passage. 

The meridian circle gives both time and altitude. 

The altitude and azimuth instrument gives the place of a star at any 
time, and in any part of the heavens. 

The equatorial mounting causes the telescope to follow a star for 
prolonged observation. 



CHAPTER VI. 

TIME, LONGITUDE, RIGHT ASCENSION. 

95. Definition. — Time is a measured portion of dura- 
tion. It is measured by some kind of uniform motion. The 
ancients measured time by the flow of water from a vessel 
called a clepsydra, or of sand from an hour-glass. We 
measure time by the uniform beats of a pendulum, or vibra- 
tions of a balance-wheel, as shown by the movement of 
hands over the dial-plate of a clock or watch. The standards 
of measure are found in the real or apparent motions of the 
heavenly bodies. 

96. Natural units of time. — Neither of the more ob- 
vious events in the sky furnishes an exact standard of time, 
because the portions of time marked by their recurrence arc 
not of uniform length. 

The natural day, whether reckoned from sunrise to sunset 
or from sunrise to sunrise again, varies in length at different 
seasons of the year. 

The changes of the moon, marking the period we call a 
month, do not occur at equal intervals, and it is difficult to 
fix by observation the exact instant of change. 

The division of the year into seasons is still more in 
definite. 

97. The solar day. — For purposes o( ordinary business, 

the passage of the sun over the meridian at noon is accepted 
as marking the middle o\~ the daw The tune from one 
passage of the sun over the meridian until the next. i> called 



5 6 ELEMENTS OF ASTRO XO MY. 

a solar day. As these intervals are not of uniform length, 
their average is a mean solar day. A clock which divides a 
mean solar day into twenty-four equal parts, called hours, is 
said to keep mean solar time. 

98. Mean and apparent noon. — The instant when 
the sun crosses the meridian is apparent noon; the hour of 
twelve shown by a clock which keeps mean solar time is 
mean noon; it may be as much as 15 or 16 minutes earlier 
or later than apparent noon. The reason will be* given in 
the articles on equation of time (233-244). 

99. The civil day begins at midnight, 12 hours before 
mean noon, and ends at midnight, 12 hours after mean noon. 

100. The sidereal day. — The successive transits of 
any fixed star, as observed by the transit instrument, occur 
at uniform intervals of 23 h. 56 m. 4.09 sec, mean solar 
time. This interval is the same at all seasons, and has not 
varied since astronomical observations began to be made. 
It furnishes the exact standard of time which we seek, and 
is called a sidereal day, or star-day. It is the time occupied 
in one rotation of the earth. 



THE ASTRONOMICAL CLOCK. 

101. The sidereal or astronomical clock is so regu- 
lated as to divide a sidereal day into twenty-four hours. It 
keeps sidereal time, or star-time. It is very carefully made, 
that it may run with the utmost regularity, and it differs from 
a common clock only in keeping star-time, instead of mean 
solar time. With the telegraphic apparatus already described 
(82), it is of the highest importance in observing transits. 

CELESTIAL CO-ORDINATES. 

102. Apparent hourly motion of the stars. — We 
have found (19, 20,) that the apparent motion of the stars is 



CELESTIAL CO-ORDINATES. 57 

due to the actual rotation of the earth ; that, while we speak 
of a star as coming to the meridian, as it seems to do, in 
fact the meridian sweeps by the star. 

In 24 hours the earth completes one rotation. In that 
time, any place on the earth— the meridian of the observer- 
has moved over 360 , passing all the celestial meridians (32) 
in succession. The meridian, therefore, moves eastward 
360 -r- 24 = 15 in one hour, 15' in one minute, 15" in one 
second. 

103. Hence, if a star culminates (47) at eight o'clock, 
and another at 15 m. 45 sec. past 8, the second star is 15 m. 
45 sec. of time, or 3 56' 15" of arc, east of the first. 

15 m. = 15 X 15' = 22 S' = 3° 45' 

45 sec. =45 X 15" = 625"= ii 7 15" 

3° 56' 15" 

The difference in right ascension (35) of two stars may be 
found from the difference in the time of their culminations. 

104. Conversely, when the difference in right ascension 
is known, the time of culmination is easily found. If one 
star culminates at 8 o'clock, when did a star culminate which 
is 25 ° 16' 19" west of the first? 

25 16' 19" -;- 15 give 1 h. 41 m. 5 T \ sec. difference of 
time. 

The star culminated at 8 h. — 1 h. 41 m. 5,*- sec. = 6 h. 
18 m. 54y3- sec. 

105. Hour-circles. — The apparent motion oi the stars 
across the meridian marks the flight of time more accurately 
than the most perfect (-lock. The are oi the equinoctial 
included between the meridians o\ two stars determines the 
time which must elapse between the transits o\ those Stars. 

The whole heavens may be conceived to be divided by celes- 
tial meridians into spaces 15 wide, and each o( these spaces 
will be traversed by the observer's meridian in one hour. 
Hence these celestial meridians are called '.. f, and 



58 



ELEMENTS OF ASTRONOMY. 



the angles which they make with each other at the poles are 

called hour-angles. 

106. Observations of right ascension. — If we say 

that a star is 15 , or that it is 1 hour east of another, we 

evidently state the same 
fact. To save reduction, 
therefore, it is customary 
to state right ascension in 
time rather than in degrees 
of arc. But the origin of 
right ascension is a point 
on the equinoctial called 
the vernal equinox (35), 
hence if the sidereal clock 
(101) reads o h. o m. o sec. 
when that point crosses the 
meridian, we have only to 
note the reading of the 
to obtain its right ascension, 
chronograph (82) as the star 




Fig. 43- 



clock at the transit of a star 

The record is made on the 

passes the vertical wires of the transit instrument, or of the 

mural circle. 

107. Observations of declination. — The microscopes 
of the meridian circle (90) read the altitude of a star at its 
culmination. The declination of the star is its meridian 
distance from the equinoctial (33), and is equal to the differ- 
ence between the altitude of the star and of the equinoctial, 
each taken on the meridian. If the altitude of the star is 
the greater quantity, the declination is north; if the less, 
south. But the meridian altitude of the equinoctial is equal 
to the co-latitude of the place of observation (Appendix I) ; 
we find, therefore, the declination of a star to be the differ- 
ence between its meridian altitude and the co-latitude of the 
observer. 

108. The celestial globe. — From the right ascension 
and declination of a star, its position may be located on a 



TO FIND LONGITUDE. 59 

celestial globe. Having a smooth spherical surface, accu- 
rately balanced on an axis, draw a great circle equidistant 
from the poles, to represent the equinoctial. Take some 
point on the equinoctial for the vernal equinox, and, begin- 
ning at this point, divide the circle into 24 equal parts, or 
hours; through the points of division and the poles draw the 
principal meridians or hour-circles (105), numbering them at 
the equinoctial from I to XXIV. 

109. To locate a star. — Take an arc on the equinoc- 
tial, beginning at the vernal equinox, equal to the right 
ascension, and through the end of this arc draw a meridian ; 
on this meridian, north or south, as the case may be, measure 
an arc equal to the declination ; the point found is the place 
of the star. A map of a part of the sky is thus made, just as 
a map of part of the earth's surface is constructed. It will 
be seen, however, that the map of the sky, on the globe, is 
the exact reverse of that which it represents on the sky. The 
globe is seen from the outside, while the sky is seen from 
within, at a point near its center. 

A fac-simile of the sky might be made on the inner surface 
of a large globe, into which the observer might go, but such 
a contrivance would be neither necessary nor useful, so long 
as the grand original may be seen nightly over our heads. 



TO FIND LONGITUDE. 

1 10. Terrestrial longitude may be determined by ob- 
servations of time. Ef a star culminates at the meridian 
of one observer one hour sooner than at the meridian of 
another, the second observer is 15° west o\ the first. 

The local time is determined for any place by the passage 
of the sun over the meridian of that place; hence the differ 

ence between the local time o\ two places, shows very nearly 
the difference between the longitude of those places. It the 



60 ELEMENTS OF ASTRONOMY. 

time used is sidereal time, the difference in time, reduced to 
degrees, minutes, and seconds, gives the difference in longi- 
tude exactly. 

As means of finding longitude is of the highest importance, 
especially to commerce, great pains has been taken to deter- 
the longitude of sea-ports, and to find methods for getting 
longitude at sea. Much of the development of the science 
of astronomy has grown out of attempts to solve these 
problems. 

in. Longitude by telegraph. — As the action of the 
electric telegraph is almost instantaneous, it furnishes a very 
exact method of determining longitudes. Connect two ob- 
servatories, as Cambridge and Chicago; record the transit 
of a star at Cambridge by the chronograph at each place; 
when the same star passes the transit wires at Chicago, let the 
record be again made by each chronograph. The time 
which elapses between the two observations, when re- 
duced to degrees, gives the difference of longitude of the 
two places. 

112. Longitude by chronometer. — A chronometer* 
is a watch made with special pains to keep time accurately, 
yet, made and regulated with the utmost care, it rarely runs 
with absolute precision. The rate of a chronometer is the 
amount which it gains or loses regularly, day by day, or week 
by week. 

The chronometer is first regulated as closely as possible ; 
then its rate is found by comparison with another whose rate 
is known, or with the movement of the stars; it is then 
set with the astronomical clock of some observatory. Hence- 
forth, wherever it may be, it shows the time according to 
the clock of that observatory, correction being made for the 
rate. Suppose, then, that a sea-captain carries New York 
time; he observes that, where he is, the sun crosses the 



Xgovo^, Chronos, time ; fikrguv, metron, 



measure. 



LONGITUDE. 61 

meridian at 5 p. m. by his chronometer; he is evidently 
5 X i5° = 75° west of the meridian of New York. 

Some years since, sixty chronometers were carried several 
times back and forth between Cambridge, Mass., and Liver- 
pool, England, in order to obtain, by averaging their results, 
the difference of longitude between the two observatories, 
and thus to connect the systems of geographical measurement 
of the two continents. 

Mariners usually depend upon chronometers for longitude, 
and have them rated with great care at every sea-port 
where time is furnished by astronomical observations. Thus, 
astronomical science becomes invaluable to the commerce 
of the world. A ship at the equator will be 15 nautical 
miles from her supposed place if her chronometer is one 
minute wrong ; at higher latitudes, the error of place will be 
less, but in either case such an error may cause disaster. 

113. Longitude by eclipses of Jupiter's satel- 
lites. — The difference of longitude between two places may 
be found by observing at one place any event in the sky 
which has been accurately predicted in the time of the other. 
The planet Jupiter is attended by four moons, which often 
pass behind the planet or are eclipsed in its shadow ; the 
times of these occupations or eclipses are predicted, and are 
recorded in a nautical almanac as they will be seen at Green- 
wich or Washington. The motion of the sea forbids telescopic 
observations of them on board ship, but on land the} are 
easily seen, and are valuable means of finding longitude. 

114. Longitude by lunar observations. — The dis- 
tance of a given star from the sun or moon, if predicted for 
a given time and place, may be used as a signal in the skv 
from which to determine longitude. To use this method, 

the mariner must have an instrument by which he can 

measure the angular distance between two heavenly bodies. 

115. The Sextant. — The general appearance of die 

sextant will be learned from the engraving. The index arm 



62 



ELEMENTS OF ASTRONOMY. 



above the frame moves about a pivot at /, where it sustains 
the index-mirror ; at the other end, it carries an index over 
the graduated scale A. At F is a mirror called the horizon- 
glass, silvered only on its lower half. The observer, holding 
the instrument by the handle behind the frame, places his 

eye at the ring K, and 
looks through the open 
part of the mirror F at 
some object, as a star. 
He then moves the index 
along the scale, until the 
image of another object, 
as the edge of the moon, 
reflected from the mirror 
/, appears in the mirror 
F exactly under the star. 
The angle between the 
moon and the star is 
shown by the part of the 
scale which is traversed 
by the index (App. II). 
At D and E are several colored glasses, used to protect the 
eye when the sun is observed; they are turned out of the 
way at other times. 

To find the altitude of a star, we look toward the horizon, 
bring the image of the star to coincide with it, and read the 
scale, making correction for the dip of the horizon (2), and 
for refraction (124). 

The sextant is of great value at sea, because its use is not 
prevented by the motion of the ship. 




Fig. 44- 



MOTION IN THE SKY. 



116, Motion among the stars. — Every point on the 
sky passes the meridian at intervals of 23 h. 56 min. 4.09 



THE ECLIPTIC. 63 

sec. solar time, or 24 hours star-time (100). If any object, 
the sun, or a star, does not re-appear at the spider-line of the 
transit instrument at the interval of a star-day, that object 
must have moved since its last culmination. To understand 
which way it has moved, we again call to mind that the earth 
rotates, not the sky. 

The Meridian, the plane of the terrestrial meridian of 
the place where we are observing (32), moves regularly to 
the eastward as the earth rotates, passing all the celestial 
meridians in succession, and coming back to its first position 
in 24 sidereal hours. If, therefore, the star has moved east- 
ward, the meridian does not find it in the old place, but 
must go on farther to overtake it, and the time between 
transits will be more than 24 star-hours. If the star has 
moved westward the meridian will pass it in less than 24 
hours. If it has moved directly north or south, the time of 
transit will not vary, but the mural circle will detect a change 
of altitude. 

117. Fixed stars are those which keep their places in 
the sky. A few stars, observed from night to night, are 
found to move from place to place, and are called wandering 
stars, or planets* 

THE ECLIPTIC. 

118. The annual motion of the sun. — The sun passes 

the meridian at intervals which average 24 h. 3 m. 56.5 sec, 
star-time. From this it appears that the sun has a regular 
motion among the stars, eastward ; and, by observing the 
stars which culminate at midnight, that is. just 12 hours after 
the sun, we find that he makes the entire circuit of the 
heavens in one vear. We have already learned (5*— 54) 

that the sun's declination changes from day to day, B) 
noting the sun's position daily on a celestial globe (109), 



* I ]/\ar//T/ / \-, Planites. a wand< 



64 ELEMENTS OF ASTRONOMY. 

from his declination and right ascension, we trace his 
apparent annual path among the stars; this we have called 
the ecliptic (58). 

In Chapter X, we will inquire if the sun actually moves in 
this path, or if his motion is only apparent, explained, like 
his daily rising and setting, by some motion of our own. 

119. Distance on the ecliptic, measured eastward from the 
vernal equinox, is called celestial longitude. Distance from 
the ecliptic, measured on a great circle perpendicular to the 
ecliptic, is called celestial latitude. It should be observed 
that celestial latitude and longitude do not correspond to 
terrestrial latitude and longitude. The celestial measure- 
ments which are similar to terrestrial latitude and longitude, 
being referred to the equinoctial, are declination and right 
ascension (33, 35). 

The solstitial colure (57) is perpendicular to the ecliptic. 
The pole of the ecliptic is on this circle, 23 ° 27' 14" from 
the pole of the equinoctial. 



I20. RECAPITULATION. 

Time, a portion of duration ; measured by uniform motion. 

Culminations of the sun measure solar days ; of the stars, sidereal days. 

Celestial meridians are hour-circles ; the angles which they make 
with each other, hour-angles. 

Right ascension may be measured in degrees of arc, or in time ; 15 
degrees are equivalent to one hour. 

^ ..... (The magnetic telegraph. 

Terrestrial longitude 

. . . The chronometer. 

may be determined by J. _ ,. 

Eclipses of Jupiter s satellites. 

Lunar observations. 

Any object in the skv which does not return to the meridian in 
twenty-four hours of sidereal time, has a real or apparent motion. 
The sun is such a body. 

The sun's apparent annual path, The ecliptic. 

Measured on the ecliptic, Celestial longitude. 

Measured from the ecliptic, Celestial latitude. 



CHAPTER VII. 

ATMOSPHERIC REFRACTION. DAY AND NIGHT. TWILIGHT. 

121. The latitude of the observer is equal to the 
altitude of the nearest pole (39) ; but, as there is nothing 
precisely at the celestial pole to mark the point, its altitude 
can not be directly observed. The stars in the northern sky 
seem to move about the pole in circles (18), and, if we find 
the altitude of one of these stars at its superior culmination 
and again at its inferior culmination, the mean, or the half 
sum of these altitudes, should be the altitude of the pole. 

122. The apparent daily paths of the stars are 
not exact circles. — With the altitude and azimuth instru- 
ment (91), we may follow a star from hour to hour, and note 
its successive positions on a chart. We shall find that its 
path, although nearly circular, is not exactly so. The Hon 
zontal diameter is longer than the vertical, and the lower 
half of the curve is a little flattened. Hence we suspecl 
that the midway altitude of a circumpolar star is not exactly 
equal to the altitude of the pole. 

123. The evidence of other stars. — If we select two 
stars unequally distant from the pole, the altitude of the pole 
found by the culminations o\ the nearer star will he less than 
that determined 1>\ the other. A star 30 or 35 degrees from 

the pole, observed in latitude |o l \ will give a result \: or 

15 minutes greater than that of the pole-star. There must 
he, therefore, some source oi error which causes the stars to 

A si 5, 



66 



ELEMENTS OF ASTRONOMY. 



seem higher than they really are, and which produces its 
greatest effect near the horizon. 



A TMO SPHERIC REFRA C TION. 



124. We have learned that a ray of light which passes 
from a rarer to a denser medium is bent toward the perpen- 
dicular to the surface of the new medium; this bending we 




have called refraction (62). But the air is rarer as the dis- 
tance from the earth increases. The ray of light which 
comes into our telescope from a star, has passed through 
many strata of air, from the rarest, which forms the highest 
part of the atmosphere, to the denser layer in which the 
instrument stands. At each increase of density, the ray has 
been bent downward, and it has come to us, therefore, in a 
path slightly curved. But the direction which the ray has 
when it enters the telescope or the eye, fixes the apparent 
position of the star ; the altitude of the star is therefore in- 
creased by atmospheric refraction. 



ATMOSPHERIC REFRACTION. 



6 7 



125. At the zenith, refraction is nothing; near the zenith, 
it increases slowly; near the horizon, rapidly. It varies also 
with the density of the air, as shown by the barometer, and 
its temperature, as shown by the thermometer. At the 
horizon, it is usually about 36' 29"; that is, a star which 
seems to be on the horizon, is really 36'. 5 below the horizon, 
and the ray of light from it, curving round the earth, causes 
its apparent elevation. The refraction at different altitudes 
is as follows:* 



Altitude. 


Refraction. 


Altitude. 


Refraction 


o° 


36' 29" 


10° 


5' 20" 


1° 


24' 54" 


3°° 


1' 41" 


2° 


18' 26" 


5°° 


0' 49" 


5° 


9' 52" 


9°° 


0' OO" 



126. Effects of atmospheric refraction. — 

1. The sun is visible when it is 36'. 5 below the horizon. 
It, therefore, appears to rise earlier and set later, by the 
length of time it takes the sun to cross this distance. At the 



POSITION mO SHAPE 
BY REFRACTION 



SUN 



ACTUAL POSITION 
HORIZON 



Fig. 46. 

equator, the day is longer on this account by about four 

minutes; at the pole, about tour days. 

2. The sun is visible on more than halt' the earth's surface 

at the same instant. The Illuminated half o( the world is 
increased by a belt or zone about 40 miles wide. 



Bessel. 



68 ELEMENTS OF ASTRONOMY. 

3. The disc of the sun or moon is somewhat distorted 
when near the horizon. The sun's disc is 32' broad. When 
the lower limb is actually in the horizon, refraction raises it 
to 36' 30"; at the same time the upper limb, whose real 
altitude is 32', is raised by refraction 27' 30": it has an 
apparent altitude of 59' 30". The apparent distance between 
the sun's upper and lower limbs is, therefore, 23', or 9' less 
than the horizontal diameter. 

127. The great apparent size of the sun and moon 
at the horizon, is not caused by refraction. It is an optical 
illusion, caused partly by an unconscious comparison with 




Fig. 47- 

intervening objects, and partly by an idea of the great dis- 
tance of the heavenly body, as compared with the distance 
of the visual horizon. Experiment shows that the disc of 
the sun or moon is not broadest when near the horizon. 

Roll a sheet of paper into a conical tube so large that 
while the eye is at the small end the rising moon shall seem 
just to fill the other; when the moon has risen some dis- 
tance, the large end of the same tube will appear to be more 
than filled by the moon's disc. If the moon should pass 
through the zenith, her diameter there would appear greater 
by this test than in any other position in the sky. 

The moon when in the zenith is actually nearer the ob- 
server than when in the horizon by a little less than the 
radius of the earth. Let an observer be at A on the earth ; 
the moon M appears in his horizon, at a distance AM, the 
base of the right-angled triangle ACM. As the earth turns 



TO FIND LATITUDE. 69 

on its axis, the observer comes into the position B, the moon 
being in his zenith. The distance to the moon is now BM, 
less than CM by the earth's radius CB, and less than AM 
by a little less than the earth's radius. 

128. Small stars are not visible near the horizon; either 
the irregular refraction dissipates their light, or the dense 
vapors near the earth prevent its passage. 

129. True altitude. — The true altitude of a star is its 
apparent altitude diminished by the proper correction for 
refraction (125). All observations for altitude, whether taken 
with the meridian circle, the altitude and azimuth instrument, 
or the sextant, require this correction. 

TO FIND LATITUDE. 
\ 

130. To find latitude by a circumpolar star. — The 

latitude is equal to the half sum of the true altitudes of any 
circumpolar star, observed at the place in question. As the 
circle of daily motion of the pole-star is smallest, that star is 
best adapted to observations of this kind. 

131. To find latitude by the sun. — The meridian 
altitude of the equinoctial equals 90 minus the latitude (51). 
The declination of the sun is its distance north or south of 
the equinoctial, measured on the meridian (33). Find the 
declination of the sun for the day of the year on which the 
observation is taken (App. Ill), and take the meridian alti- 
tude of the sun with the meridian circle or the sextant (1 15). 
If the sun is in north declination, subtract the declination 
from the altitude; if in south, add the declination to the 
altitude; the result in each case is the meridian altitude of 
the equinoctial, which, taken from 90 , gives the latitude 
of the place. This method is usually adopted at sea. 

/)./)■ AND NIGHT. 

132. Relative length of day and night. The daily 
apparent path of the sun in the sk\ is a circle o\ daily 



70 ELEMENTS OF ASTRONOMY. 

motion parallel to the equinoctial (31). That part of the 
circle which is above the horizon is the diurnal arc ; that 
which is below, the nocturnal a?r. The ratio between them 
is the ratio between day and night. 

133. At the equator, where the equinoctial is perpen- 
dicular to the horizon (38), the circles of daily motion are 
equally divided; hence the sun is as long above as below 
the horizon, during each twenty-four hours of the year, and 
the day is always equal to the night. 

134. At the pole, where the equinoctial coincides with 
the horizon (37), the circles of daily motion are either wholly 
above, or wholly below, the horizon. When the sun's decli- 
nation is of the same kind as the pole in question, he is above 
the horizon; when of the opposite kind, he is below. As 
the sun has north declination half the year, the day at the 
north pole lasts six months, and the night six months. 

135. When the sun is at the equinox, his circle 
of daily motion is the equinoctial. But the equinoctial and 
the horizon, being both great circles on the sky (8, 31), 
divide each other into semicircles (55); hence the day is 
equal to the night throughout the world, save at the poles; 
there the sun, being on the horizon, is making the transition 
between day and night. 

136. In north latitude. — The diagram shows the posi- 
tion of the circles of daily motion at 40 ° north latitude. It 
is evident that of two circles, parallel to the equinoctial, 
that which is farthest north has the largest proportional part 
above the horizon. Hence, at this place : 

1. The day is longer than the night when the sun's decli- 
nation is north, and conversely when it is south. 

2. The length of the day increases as the sun moves north- 
ward until he reaches his greatest northern declination on 
the 20th of June (51); the days become shorter as the sun 
moves southward until he reaches his greatest southern 
declination on the 2 2d of December (52). 



CIRCLES OF BAIL Y MOTION. 



71 



137. Farther north. — As the observer goes north from 

the equator, the angle between the equinoctial and the 

horizon becomes less; the circles of daily motion lie more 

obliquely; those north of the equinoctial show a rapidly 




Fig. 



increasing diurnal arc ; the proportion in those south of the 
equinoctial decreases as rapidly ; long days become longer, 
and short days shorter. At 66° 32' north latitude the circle 
of daily motion on the longest day o( the year coincides 
with the circle of perpetual apparition (42) ; for. as the 
declination is 23 27'. the north polar distance is oo° $2* 
(34), which is equal to the latitude. On the 20th ol lune. 



72 ELEMENTS OF ASTRONOMY. 

therefore, the sun does not set. Farther north, the sun will 
not set so long as his declination is more than the distance 
in degrees and minutes from the place of the observer to 
the pole, or more than the co-latitude. 

138. In the southern hemisphere, all the results 
described for the northern hemisphere are reversed. The 
sun passes from east to west through the northern sky; he 
casts all midday shadows toward the south; the longest 
days are in December, and the shortest are in June. 

139. The amplitude (12) of sunrise and sunset. — 

The diagram also illustrates the variable position of the sun 
at sunrise and sunset. When on the equinoctial, the sun 
rises exactly in the east and sets precisely in the west. As 
his declination increases northward, the places of both sun- 
rise and sunset move toward the north, and this movement 
increases with the latitude. At the polar circle, the sun on 
the longest day merely touches the horizon at the north 
point, setting and rising again the next instant. On the 
shortest day, when his declination is south, he appears but 
for an instant at the south point, rising and setting again 
immediately. 

140. Corrections. — If we seek the exact time or place 
of sunrise or sunset, corrections must be made : 

1. For the effect of atmospheric refraction (129). 

2. For the breadth of the sun's disc. 

Hitherto reference has always been made to the center 
of the sun's disc. But sunrise comes at the instant when 
the first ray crosses the horizon, and sunset is delayed 
until the last ray vanishes from the upper limb. Hence, 
as the sun's disc is 32' broad, sunrise occurs when the sun's 
center is 16' below the horizon. 

The effect of both these corrections is to lengthen the 
day, and to shorten the night in all parts of the world. 



TWILIGHT. 



73 



TWILIGHT. 

141.. Daylight does not instantly vanish at sunset; it 
fades away gradually, passing through all the shades of 
waning light which we call twilight. This is caused by the 
reflection of the light from the upper regions of the air. 
Let the curve ACEF represent the surface of the atmos- 
phere which surrounds the earth, and suppose the light 
comes from the sun in the direction indicated. No direct 




Fig. 49- 



rays of sunshine come to the earth beyond the line AF. 
but some portion of the atmosphere is illuminated as far 
as the line BE. The observer at A sees the sun in his 
horizon. The sun has set for the observer at />, but he 
sees some reflected sunlight from the space between A and 
/>'. For the observer at (' both direct and reflected light 
have vanished. 

The twilight which precedes sunrise is called the dawn. 

142. Duration of twilight. — Twilight continues until 
the sun is 1S below the hori/on; some writers sa\ 24°. 
Its duration must vary somewhat with the condition of the 
air. The /one which is thus partially lighted is about 1250 
miles wide. 



74 ELEMENTS OF ASTRONOMY. 

The duration varies with the latitude. At the equator, 
where the daily path of the sun is at right angles to the 
horizon, the twilight zone is passed in i h. 12 m. All 
travelers in equatorial regions remark the very brief time 
between sunshine and the darkness of night. As the lati- 
tude increases, the sun's path crosses the zone more ob- 
liquely, and twilight lasts longer. At lat. 48 ° 30', on the 
night of the Summer Solstice, twilight lasts from sunset to 
sunrise; at higher latitudes this happens on several nights in 
succession. At the pole, twilight mitigates the long win- 
ter night until the sun has reached a declination 18 on 
the opposite side of the equinoctial, or for about 75 days. 

143. The crepuscular curve. — Lacaille claimed to 
have actually seen, while at sea in the South Atlantic, the 
shadow of the earth forming a curve on the sky opposite 
the sun, and following the sun toward the west as the twi- 
light faded. This curve which separates the illuminated 
portion of the sky from the darker part is called the crepus- 
cular curve. If seen at all, it must be under the most favor- 
able circumstances and in the clearest air. 

144. The height of the atmosphere. — Twilight would 
last longer if the layer of air about the earth were thicker, 
or if its upper strata were denser than now. If the crepus- 
cular curve could be clearly seen, the thickness of the 
atmosphere might be easily computed; on the supposition 
that twilight lasts until the sun is 18 below the horizon, 
the height of the atmosphere would be about 40 miles. 
But the density of the air diminishes with its height above 
the earth, and in its upper regions it doubtless becomes too 
rare to reflect much light, if any. Hence, the air may be 
presumed to extend considerably above that distance. 

Without the quality in the air which produces the diffusion 
or dispersion of light, there could be no twilight; every place 
not in direct sunshine would be utterly dark, even in the 
daytime. 



TWILIGHT, 



75 



145. 



RECAPITULATION. 



The altitude of the celestial pole is found from the culminations of 
circumpolar stars. 

Correction is required for atmospheric refraction ; it increases the 
apparent altitude of a celestial object, especially when near the 
horizon. 

Terrestrial latitude is found : 

1. By culminations of circumpolar stars; 

2. By meridian altitude of the sun rb declination. 
Day = night 

the sun's 



At the equator, where 
At the poles, where 
Elsewhere, when 

Day ^> night 
Elsewhere, when 

Day <C night 
Elsewhere, when 



daily 
path is 



in the observers hemisphere. 

in the opposite hemisphere. 
Twilight is caused by reflection of light from upper region of 
atmosphere; it lasts until the sun is 18 below the horizon. 



perpendicular to the horizon. 
parallel to the horizon, 
on the equinoctial. 



CHAPTER VIII. 

SHAPE OF THE EARTH. GRAVITATION. 

146. Public surveys. — The construction of accurate 
maps is a matter of national importance. When a boundary 
line between two states or nations is not fixed by some natural 
landmark, as the channel of a stream, or the crest of a mount- 
ain, it is often made at lines of latitude and longitude ; these 
must be determined astronomically. The bounds of many 
of the states and territories, as well as those between the 
United States and the British Provinces and Mexico, are 
fixed at astronomical lines. 

Our sea-coast is long and dangerous. The ships which 
annually enter our harbors, or leave for foreign or domestic 
ports, bear hundreds of thousands of lives, and about two 
thousand millions of merchandise. The nation should em- 
ploy every means, practical or scientific, by which danger 
may be avoided, and safety insured. To this end, it is 
necessary to determine the coast-line, and to observe the 
changes going on there and at the sea-bottom within sound- 
ings; to ascertain the laws which govern currents, tides, and 
winds; to locate light-houses and other signals; and to pub- 
lish results in reliable maps and charts. For many years 
our government has conducted such a survey along the sea- 
board, and has extended it by the great lakes and rivers 

across the continent. 

(76) 



TRIANG ULA TION. 



77 



TRIANG ULA TION. 



147. It is first necessary to determine the latitude and 
longitude of prominent points along the coast, as hills, spires, 
and head-lands, and to find the distances between them. A 
base-line is measured on a piece of level ground, usually 




Fig. 50. 



from six to ten miles long, and the ends of this line are 
located astronomically. This line is made the base of a 
triangle whose vertex is on a distant hill; the angles at the 
base are observed, and the two opposite sides are found by 
the methods of trigonometry. These lines are used as bases 
of other triangles, which are solved in the same way. Thus 

the triangulation continues until every conspicuous object m 

the whole country is included in the s\stem. 



78 ELEMENTS OF ASTRONOMY. 

148. Example. — Suppose that signals have been erected, 
and a base-line, 12, Fig. 50, has been measured, six miles long, 
From the stations 1 and 2, the angles 213 and 123 have been 
observed, and the distances 13 and 23 are computed. 23 is 
now the base of the triangle 234; 43 is found, which be- 
comes the base of 345, and so on to stations 6 and 7. The 
line 23 may also be the base of the triangle 236, and thus 
the station at 6 will be located by two operations which 
should prove each other. 

149. Another proof. — After the work has progressed 
over a large district, a new base is measured, or the triangles 
are made to connect with those begun at another line; the 
agreement of the computed and measured lengths tests the 
accuracy of the work, including observations, measurements, 
and computations. A base-line in Massachusetts, on the 
Boston and Providence Railway, 10.76 miles long, has been 
connected by triangulation with base-lines at Epping, in 
Maine, and at Fire Island, south of Long Island. The 
distance from 

Epping Base to Mass. Base is 295 miles 
Mass. Base to Fire Island Base 230 " 
Length of Mass. Base, measured, 56846.09 feet. 

" computed from Epping Base, 56846.59 " 

" Fire Island Base, 56846.32 " 
First difference, in 10.76 miles, 6 inches. 
Second " " " 2.8 

150. Measuring apparatus. — The base-lines of the 
U. S. Coast Survey have been measured with the greatest 
accuracy by an apparatus devised by Prof. A. D. Bache. 
The rod is a compound bar of iron and brass, so adjusted 
that the change of length in one part, on account of heat 
or cold, is exactly counterbalanced by a change of length 
in the other. The rod is inclosed in a spar-shaped case, 
painted white to reflect the heat of the sun. Two such 



TRIANGULA TION. 



79 



rods are laid in line upon tripods, properly placed, and the 
contact between the ends is shown by the motion of a very 
delicate level. Any necessary deviation from a straight or 
level line is observed and corrected by computation. 




Fig. 51. — Bache's Measuring Apparatus. 






Compensation End. 



Fig. 52. 



Sector End. 



a, a, the iron rod; />, />, the brass rod; c, the lever of compensation, hinged 
to the brass and resting against the iron; d, <i", sliding rods, which meet in 
agate surfaces at E; the rod df pushes at /against the lover of contact, which 
brings the spirit-level g into a horizontal position. The slope is shown by the 
graduated scale /, which is moved by the screw k, until the spirit-level '■■ i- 
horizontal. The screw / brings the rods together. 



151. Completion of survey. — After the principal tri- 
angulation has located the prominent points, miner places 
are determined in a similar way, and are located on a map. 

The coast line is then filled in, soundings are taken oil 
shore, rocks, reefs, and shoals are marked, suitable channels 
are indicated, and sailing directions added, by which the 
mariner may steer his craft to a safe anchorage. 



8o 



ELEMENTS OF ASTRONOMY. 



Similar surveys have been made in Great Britain and in 
continental Europe, and have been commenced in India and 
in South America. 



THE SHAPE OF THE EARTH. 



152. The length of a degree of latitude. — A degree 
of latitude is such a distance, measured on the meridian, as 
shall increase the altitude of the pole one degree (40). By 
the methods described, the length of a degree of latitude has 
been found in various places, and at various distances from 
the equator, from Peru, lat. i° 31', to Lapland, lat. 66° 20'. 
Among the results are the following : 



Place of 
measurement. 



Lat. 



i° 3i' 



Peru, 

India, 16 08 22 

United States, 39 12 00 

England, 52 02 20 

Lapland, 66 20 10 



153 

table, 



Length of 
degree in feet. 

362,790 

363 ? 44 

363,7^ 

364,95! 

365,744 

# miles = 365,440 



Measured by. 

Bouguer. 
Lambton. 
Coast Survey. 
Roy; Kater. 
Svanberg. 



center 



, The earth flattened at the poles. — From the 
it appears that a degree of latitude is shortest near the 
equator, and becomes longer as we 
approach the pole. But since near the 
equator the altitudes of the pole mark 
degrees by measuring shorter spaces, 
it is evident that we must be moving 
on a smaller circle, with a sharper 
curvature; near the pole the measured 
degree is longer, the curve must be 
part of a larger circle, of less rapid 
curvature. In the diagram, draw ab, 
one third of a quadrant, from the 
1; take a new center, 2, in the line b\ prolonged, and 




Fig. 53- 



ATTRACTION OF GRAVITATION. 8 1 

draw be, one third of a quadrant; take a new center, 3, in 
c 2 prolonged, and draw ed, one third of a quadrant. It is 
evident that the arc ab is less than be, and still less than cd, 
since each is drawn from a nearer center, yet each is oppo- 
site an angle of the same amount, as each arc is one third 
of a quadrant. Hence we see that the curvature of the 
earth is less at the pole than at the equator; that is, the earth 
is an oblate spheroid. 

154. Dimensions. — Geodetic surveys in different parts 
of the earth have been collated, and, as additional material 
is found, the results vary, as in the following table: 

Diameters. Airy, 1831. Bessel, 1841. Clarke, 1880. 

Equatorial, 7925.648 7925.604 7926.581 

Polar, 7899.170 7899.114 7899.592 

Difference, 26.478 26.490 26.989 

The center of the earth is 13.5 miles farther from the 
equator than from the pole. If the earth were represented 
by a globe one yard in diameter, the polar diameter will be 
about T X y- of an inch too long. 

Results lately obtained indicate that the equator is not an 
exact circle, but that the diameter which passes from longi- 
tude 8° 15' west, to 17 1° 45' east of Greenwich, is longer 
than the diameter at right angles to it by \ of a mile. The 
equatorial diameter given above is the mean. 



ATTRACTION OF GRAVITATION. 

155. Any body, as a stone, unsupported, falls to the earth. 
But no bod)' has power to move itself; hence the stone comes 
to the earth because the earth draws it. or because the two 
mutually draw each other. The mutual attraction of matter 
at all distances is called the attraction of gravitation, or simpl] 
gravity. The weight oi a body is the measure o( the earth's 
attraction. A roll oi butter weighs a pound if the earth's 

A M -6. 



82 



ELEMENTS OF ASTRONOMY. 



attraction for it is the same as for a piece of iron of a certain 
size which we call a pound. 

156. Gravity is in proportion to the mass. — By the 

mass of a body is meant the sum of the particles which com- 
pose that body, without reference to its size or bulk. If one 
particle draws with a certain force, two particles will exert 
twice that force, and a thousand particles, a thousand fold; 
the attraction of the whole is the sum of the attractions of 
all its parts. In like manner, its attraction for two particles 
will be twice that for one, and so on. Hence, at the same 
distance, 

The attraction for one body : the attraction for another : : 
the mass of the first body : the mass of the second; or 

G : G' : : M : M' . 

157. Gravity diminishes in proportion to the 
square of the distance. — The attraction of a particle 
goes out from it in every direction : it lies in the center 




Fig- 54- 



of a sphere of attraction. A surface at some distance, as at 

B, receives so much of the attraction from P as is included 
within the lines 1, 2, 3, and 4; but the surface at C receives 
the same amount of attraction since it lies within the same 
lines. If the distance from P to B is 1 unit, and from P to 

C, 2 units, the surface at C equals four times that at B. 
Now, if B were removed to C, it would occupy only one 
fourth the space of C, and would receive from P only one 



RADIAL AND TANGENTIAL FORCES. 83 

fourth the attraction received by C, that is, one fourth the 
attraction which it now receives. At 3 times the distance it 
would receive J the attraction; at 10 times the distance, T -^g- 
the attraction, and so on. Hence, for the same mass, gravity 
is inversely as the square of the distance, or, 

G : G> : : -i- : -*-. 

158. The general law. — Combining the two preceding 
results, we have the general law: — The attraction of gravi- 
tation is directly as the mass and inversely as the square 
of the distance. 

Z> 2 Z>' 2 

Newton proved that the sum of the attractions of the 
particles which compose the earth may be considered as 
acting at the center of the earth; as if all the particles with 
their, attractive force were condensed into one at the center. 
Hence, the distance at which the earth's attraction acts is 
reckoned from the center, and the weight of a body attracted 
by the earth will vary inversely in proportion to the square 
of its distance from the center. 



RADIAL AND TANGENTIAL FORCES. 

159. Whenever a body, A, moves about a center, C\ it 
obeys two forces, one holding it to C, the other striving to 
drive it along a tangent toward B. The first may be called 
a radial force; the second, a tangential force; they arc also 
called centripetal and centrifugal forces. When a stone tied 
to a string is whirled about the hand, the impulse given the 
stone is the tangential force; the strength of the string is the 
radial force. If the Stone is whirled too swiftly, the radial 
force is too weak to answer its purpose, the string breaks. 



8 4 



ELEMENTS OF ASTRONOMY. 



TANGENTIAL FORCE 

~x— — ^ 



and the stone flies off in a tangent from the point where it 
happens to be at the instant of breaking. Even if the string 
does not break, it is strained by the whirling stone. 

160. Tangential force is produced by the rotation 
of the earth. — A point on the equator passes through about 

25,000 miles in 24 hours; it 
moves rather more than 1000 
miles an hour. A particle at 
the pole simply turns about 
in the same time. A particle 
anywhere in the mass of the 
earth, either upon or below 
its surface, moves at a speed 
which is in proportion to its 
distance from the axis. But 
the greater the speed the 
Fig. 55. greater the tangential force, 

and hence the radial force, 
which is the weight of the body, is diminished by the tan- 
gential force produced by the rotation of the earth. 




ABD represent the earth ro- 



161. Illustration. — Let 

tating upon its axis BD. 
Suppose a tube AC passing 
from the surface of the earth 
at the equator to the center, 
meets there another tube 
from the pole, and let the 
two tubes be filled with 
water. When the earth is 
at rest, each particle of 
water in one tube balances 
that in the other tube at the 
same distance from the cen- 
ter, since both are attracted 
by the same force acting at the same distance. As the earth 




THE SEA -LEV EL. 85 

rotates, the particles in CD, near the axis, have very little 
motion, and therefore little tangential force, while those in 
AC receive more and more tangential force, in proportion 
to their distance from the center. Hence the weight of the 
particles in AC is slightly diminished, and therefore a longer 
column is required to balance the weight of CD, or, as the 
two communicate, some will pass from CD into AC, until 
the two again counter-balance. The length of CD is dimin- 
ished; that of AC is increased. But the same would be 
true of other tubes similarly placed, or of the entire earth, 
if it were composed of fluid substance. The fluid near the 
equator would lose part of its weight in consequence of the 
rotation and would rise, while the fluid at the poles would 
sink proportionally. 

162. The interior of the earth is a fluid. — When- 
ever a mine or an Artesian well is sunk into the earth, the 
temperature, commencing about 100 feet below the surface, 
is found to increase from that point at the rate of one degree 
of Fahrenheit for every 55 feet in depth. From this, and 
other reasons, it appears that at the depth of a few miles 
the heat must be sufficient to melt any known substance. 
The earth is, then, a mass of melted material, covered 
with a relatively thin crust of solidified substance. The 
surface of the crust must conform lo the surface of the 
melted matter beneath, that is, to the shape which a fluid 
mass of the size of the earth and rotating so rapidly, 
would assume. 

This theory has been disputed, but not controverted. 



77/ A' SEA-LEVEL, 

163. Were the earth at rest, its particles, being free to 
arrange themselves in obedience to their mutual attraction, 

would seek to be equally distant from its center, that is. 



86 ELEMENTS OF ASTRONOMY. 

they would form an exact sphere. But we have found (152- 
154) that it is an oblate spheroid, and in its rotation we have 
found a reason for this shape. 

Rotation and gravitation, acting together, give the sea a 
spheroidal surface called the sea-level. To this surface, all 
geographical measurements of height are referred. One 
mountain-top may be 13^ miles farther than another from 
the center of the earth, yet if both are at the same distance 
above the sea-level they are said to have the same height. 

164. Weight at the equator and at the poles. — 

Any mass weighed at the equator by an accurate spring 
balance is found to weigh more when carried to high lati- 
tudes; its greatest weight would be found at the pole. 

The mass is farther from the center of the earth at the 
equator than at the pole, therefore the earth's attraction for 
it is less (157). The tangential force produced by rotation 
counteracts part of the attraction, and also diminishes weight 

(160). 

The mass loses for the first cause about ^q', for the 
second, ^g-g-; in all about T -^ ¥ of its weight; that is, 194 
pounds at the equator weighs about 195 pounds if carried 
to either pole. This accords with experimental evidence. 
The difference in weight would not be shown by ordinary 
scales, since the pieces of metal used as weights are affected 
in the same proportion as the thing weighed. 

165. The pendulum beats because of the earth's attrac- 
tion. As the attraction is less at the equator, the pendulum 
should beat slower there than at the pole, or than at any high 
latitude. This theoretical inference accords with fact, as 
shown by experiment in various latitudes. 



THE PLUMB-LINE. 

166. The plumb-line is usually said to point to the 
center of the earth. It is found to be always exactly 



THE PLUMB-LINE. 



87 




Fig. 57- 



perpendicular to the plane of the horizon; or, to a plane 
tangent to the surface of the earth at the point of obser- 
vation. Were the 
earth a sphere, this 
perpendicular line 
would always pass 
through the center; 
but because of the 
actual shape of the 
earth, it passes 
through that point 
only when the plum- 
met hangs at the 
equator or at the 
poles; elsewhere, it 
tends to a point 

which is away from the center and in the same hemisphere 
as the place of observation. At A and B the plumb-line 
tends toward C ; at D it tends toward a point F y in the 
same hemisphere ABH. 

167. The true zenith is the point in which a line drawn 
from the center of the earth through the observer, would 
pierce the sky. The apparent zenith is the point where the 
plumb-line, prolonged, would pierce the sky. At all places, 
therefore, not on the equator or at the poles, a correction lias 
to be made, varying in different latitudes, whenever the true 
zenith is to be accurately determined. 

168. Explanation. — A rigid proof of the cause oi the 
deviation of the plumb-line involves the use o\ mathematical 
methods far beyond the scope of this book, but the general 
statement is as follows: In the figure above, the plummet at 
D hangs perpendicularly to the tangent DT t and therefore 
does not point to C\ but along the line P /■'. The mass o( 
the earth to the left oi /)/•'. is evidently larger than the mass 
to the right, hence (156) its attraction is greater; bin the 



88 ELEMENTS OF ASTRONOMY. 

mass on the left is, as a whole, farther from D than the mass 
to the right, hence (157) its attraction should be less. It is 
evidently possible that the attraction of the mass to the left 
is as much less on account of its greater distance, as it is 
greater by reason of its greater mass, and that the attractions 
of the two portions, considering both mass and distance, are 
equal. This is the case, and therefore the plummet takes the 
direction DF, in equilibrium between the attractions. 



THE MASS OF THE EARTH. 




The earth's size and shape being determined, the astron- 
omer next seeks to know its mass or quantity of matter. 

169. Maskelyne's experiment.— 

Maskelyne observed a plumb-line on 
opposite sides of the mountain Sche- 
hallien, in Scotland, noting particularly 
the place of apparent zenith (167) for 
each station. From the distance be- 
tween the two stations, he found that 
the two plumb-lines should make with 
each other an angle of 41 seconds, if 
no mountain were between. But the 
apparent zeniths of the two places were 
53 seconds apart on the sky. Hence 
it appeared that the attraction of the 
mountain had drawn the two plummets 
1 2 seconds out of the lines of the earth's 
attraction, or 6 seconds on each side of 
the mountain, and from this he found 
the force of the mountain's attraction 
as compared with the force of the 
earth's attraction. From the amount 
of attraction, the mass was found by 
the laws of gravitation. 



Cjj 

Fig. 58. 



THE MASS OF THE EARTH. 



89 



170. Cavendish's experiment. — Cavendish found the 
mass of the earth thus. He hung a ball of lead, two inches 
in diameter, at each end of a light wooden beam, suspended 
by a fine silver wire. He then placed a stout bar of metal, 
which sustained two balls of lead one foot in diameter, in 
such a position that the large balls were on opposite sides 
of the small balls. The whole apparatus was carefully 
inclosed, to prevent the influence of currents of air, or 
variation of temperature, and observations were made with 




F»g 59- 

AB, the small leaden balls on the rod C; DE, the suspending wire; FG, the 
large leaden balls in the first position ; UK, the same in position on the Other 
side of the small balls. 



a telescope furnished with spider-lines. When the large 
balls were placed by the small in one position, the small 
balls were drawn aside by a certain amount; when the large 
balls were in the opposite position, the small balls were de- 
flected accordingly. The force which the large balls exerted 
in twisting the silver wire to draw the small balls out of place, 
indicated the relation between the mass of the large balls, and 
the mass of the earth. The experiment has been carefully 

repeated, both in France and England. 



90 ELEMENTS OF ASTRONOMY. 

171. Airy's experiment. — Airy observed the beating 
of a pendulum at the top and the bottom of Harton Coal 
Pit. The pendulum at the bottom of the mine was found 
to beat faster than that at the mouth. If the earth were 
of uniform density, attraction would decrease as the dis- 
tance from the center decreases; but the density of the 
interior may be so great as to increase the attraction. (App. 
IX.) From the results of this experiment, the density of 
the whole earth was computed. 

172. Results. — The results of these experiments are not 
given in weight, but by comparing the weight of the whole 
earth with its weight if composed of water; that is, by giving 
the comparative density of the earth. 

The density, as found by 

Clarke, with plumb-line near mountain, 5.316 

Maskelyne, " " " " 4.713 

Cavendish, with leaden balls, 5-448 

Reich, " " " 5.438 

Baily, " " " 5.660 

Airy, with pendulum, 6.565 

Average result, 5^, 5.523 

Baily's result, 5^3, is that usually accepted. 

The astronomer has now found the units with which he 
means to measure the universe and weigh the bodies which 
traverse it. His measuring rod is the radius of the earth; 
the weight of the earth is his counterpoise. 



173. RECAPITULATION. 

A degree of latitude is longest near the pole ; the earth is flat- 
tened at the pole, — is an oblate spheroid. 

The spheroidal shape is caused by rotation. Rotation develops 
tangential force, which diminishes weight. The rapidly rotating 



R EC API TULA TION. 9 1 

material at the equator is heaped up until its loss in weight is 
balanced by its increased bulk. 

A body loses weight when carried from the center of attraction. 
If taken from the pole to the equator, it loses weight because both 
of its rotation and of its greater distance from the center of the 
earth. 

A pendulum beats slowest at the equator for the same reasons. 

The mass, and thence the density, of the earth, have been found : 

By Maskelyne, with a plummet, near a mountain. 

By Cavendish, with leaden balls. 

By Airy, with the pendulum. 



CHAPTER IX. 

THE DISTANCE OF THE HEAVENLY EODIES. 

174. We have already seen (147), that from the length 
of a base-line and the angles at either end, between the 
base and lines of sight to a remote point, the position and 
distances of that point may be determined. By the same 
method, the distances of the heavenly bodies may be de- 
termined. 

175. Parallax. — The angle formed at a distant object 
by lines of sight drawn to two known points is the parallax 



7o B'"at.an. 




INFINITE DISTANCE 



Fig. 60. 



of that object. Thus the angle ABC is the parallax of the 
point B. The angle of parallax increases with the length 
of the base and diminishes with the distance of the object. 
The object may be so distant that the parallax is too small 
to be measured even when the longest base is employed 
which circumstances will admit. The longest base which 

the astronomer can find in the earth is its diameter. The 

(92) 



THE DISTANCE OF THE MOON 



93 



radius of the earth is taken as a convenient unit for ex- 
pressing large distances. 

THE DISTANCE OF THE MOON. 

176. The parallax of the moon is found from observations 
taken at the same time at the ends of the longest practicable 
base, as the line which joins the observatory at the Cape 
of Good Hope, with that of Greenwich, or of Berlin. These 
observatories are favorable for this purpose because they are 




Fig. 61. 



nearly on the same meridian, and therefore the moon may 
be in the field of the meridian circle at each place at nearly 
the same instant; proper corrections arc made for the differ- 
ence of time, whatever it may be. 

Let B represent the place of the observer at Berlin; //. 
that of the observer at the Cape of Cood Hope; .1/, the 
moon, and (\ the center ^\ the earth. The angle at C 
equals the sum of the latitudes o( the two places. The 

angle CBM is found by subtracting .!//>' /, the zenith dis- 
tance of the moon at Berlin, from [8o°: the angle CUM. 



94 



ELEMENTS OF ASTRONOMY. 



similarly, by taking MHZ' from 180 . But the four angles 
of a quadrilateral together equal 360 (Geom. 346), hence 
360 — (C -f B + H) = M. The four angles of the figure 
being known, and the sides CB and CH being radii of the 
earth, the distance CM is easily found by the theorems of 
trigonometry. 

177. Lunar parallax. — The angle at the moon when 
the base-line is the radius of the earth is the lunar parallax. 
Its value at the mean distance of the moon is found to be 
57' 3"; and, the base being a unit, the distance of the moon 
which gives that parallactic angle is 60; that is, the distance 
of the moon is sixty times the radius of the earth; in round 
numbers, 60 X 4000 = 240,000 miles. 



THE DIAMETER OF THE MOON. 

178. The angle at M, which has just been called the lunar 
parallax, is also the angle which the radius of the earth would 
subtend to an observer at the moon. Hence, if seen at the 




Fig. 62. 



moon, the earth would show a disc about 114' broad. But 
the moon shows to us a disc about 32' broad, as measured by 
our micrometers (89). When two bodies are at the same 
distance from us, we readily understand that their real 
diameters are in proportion to their apparent diameters, 
hence we conclude that : 



THE DIAMETER OF THE MOON. 



95 



The apparent diameter of the earth as seen from the moon : 
The apparent diameter of the moon as seen from the earth : : 
The real diameter of the earth : The real diameter of the 

moon; 
Or, 114/ : 31' : : 7912 : 2160 = moon's diameter in miles. 

Accurate measurements give the diameter 2159.6 miles, or 
rather more than one fourth the diameter of the earth. 

179. The volume of the moon. — The volumes of 
spheres are to each other as the cubes of their diameters 
(Geom. 806). 

Vol. of E : Vol. of M : : 7912 3 : 2153 3 : : 1 : fa -f ; 
The moon is about fa as large as the earth. 

From the principle that the surfaces of spheres are as the 
squares of their diameters, we find that the surface of the 
moon is about y 1 ^ that of the earth. 




Fig. 63. 



180. Horizontal parallax. When one side of the par- 
allactic angle is in the horizon, the parallax is tailed hon 
parallax, it is also defined as the displacement which a 



g6 ELEMENTS OF ASTRONOMY. 

body in the horizon would have, if seen from the center 
of the earth rather than from its surface. 

181. Effect of parallax upon altitude. — When the 
moon is rising, its center, to an observer at A (Fig. 63), is in 
the line AB, while from the center of the earth it would appear 
in the line CD, the angle AMC being equal to the lunar par- 
allax 57'. But the angle AMC is equal to the angle MCH 
(Geom. 125); therefore, when the moon comes to the ap- 
parent horizon, having no apparent altitude, its altitude above 
the real horizon is 57'. The effect of parallax is to diminish 
altitude. This effect decreases as the altitude increases, and 
is nothing when the body observed is in the zenith. Paral- 
lax causes the moon to rise above the apparent horizon later, 
and to set earlier, than the time of passing the real horizon; 
the effect is opposite to that of refraction (126). 



ORBIT OF THE MOON. 

182. The distance of the moon variable. — The disc 
of the moon has not always the same apparent breadth. As 
we can not suppose that its actual size varies, we must con- 
clude that when it appears smaller, it is more distant. The 
breadth of disc varies inversely as the distance ; or, 

1st disc : 2d disc : : 2d distance : 1st distance. 

Computations of parallax (175) also show that the moon's 
distance is variable. 

183. The moon revolves about the earth. — By 

noting the distance from the moon to some near star, we find, 
even in an hour or two, that she moves toward the east. 
Early in the month she appears near the sun in the west, 
soon after sunset. Day by day she moves eastward, until, 
in about 14 days, she is on the side of the earth opposite 
the sun ; following her still farther, we find her again between 



THE ELLIPSE. 



97 



the earth and the sun. Thus we follow her quite around the 
earth. 

184. A plan of the moon's path may be made. — 

Draw a straight line, AB, of any convenient length, to rep- 
resent the distance of the moon on any day, say the first 
after the new moon. On the next day, find how many 
degrees the moon has 
moved eastward among 
the stars (103), and rep- 
resent this change of 
place by the angle BA C. 
From the variation in the 
breadth of the disc, find 
the change of distance 
(182), and measure this 
distance on AC, using 
the same scale with which 
we laid off AB. The 
point, C, shows the place 

of the moon for the second day. In the same way find the 
points, D, £, F, etc., for the entire month; the curve which 
connects these points is a plan of the moon's path or orbit. 




Fig. 64. 



THE ELLIPSE. 



185. What is the curve of the moon's path?— If 
it is a circle, the earth can not be at the center, for the 
distances are unequal. The principles of geometry show 
that this curve is an ellipse^ and. as we shall have frequent 
occasion to refer to that figure, we will consider its forma- 
tion and some of its peculiarities. 

186. To draw an ellipse.- Set two pins a little dis- 
tance apart, in a plane surface o( board or paper. Tie to 
each pin one end of a thread which is somewhat longer than 
the distance between the pins, and placing a pencil against 

A st. —7. 



9 8 



ELEMENTS OF ASTRONOMY. 



the thread, draw it about the pins, as shown in Fig. 65. 
The curve described is an ellipse. 




Fig. 65. 



187. Definitions. — Observing that the length of the 
string is constantly the same, we say : An ellipse is a curve 
such that the sum of the distances from any point of the 
curve to two fixed points within, is invariable. The space 

included is called an ellipse 
as well as the line which 
includes it. 

Each of the fixed points 
is a focus. 

A line drawn through 
the foci and terminated by 
the curve is the major axis. 
The middle point of the 
major axis is the center of 
the ellipse. Any line drawn 
through the center and ter- 
minated by the curve is a 
diameter. The major axis is therefore a diameter. 

The minor axis is the diameter which is perpendicular to 
the major axis. Any line drawn from either focus to the 
curve is a radius vector. 




THE ELLIPSE. 99 

The distance from the center to either focus is the eccen- 
tricity* of the ellipse. 

188. Deductions. — A little study of the figure shows: 
i. That the radii vectores vary in length from the shortest, 
equal to half the major axis less the eccentricity, to the 
longest, equal to half the major axis plus the eccentricity. 

2. That the sum of the radii vectores which meet at any 
point of the curve is equal to the major axis. 

3. That if the foci are distant from each other, that is, if 
the eccentricity is great, the ellipse is long and narrow; if the 
foci are brought near each other, the eccentricity becomes 
less, and the figure becomes more nearly round; if the foci 
are brought together, the eccentricity becomes nothing, and 
the ellipse becomes a circle. Finally, if the foci are placed 
at the ends of the major axis, the ellipse collapses into a 
straight line. Hence, an ellipse may have any form between 
a circle and a straight line. 



189. RECAPITULATION. 

Parallax is the angle formed by two lines which meet at a distant 
body, as the moon. From parallax, distance is found. 

The parallax of a body is the angle subtended by the base of paral- 
lax as seen from that body. From parallax and apparent size, actual 
size is found. 

From apparent size and angular motion, as (hoy vary from time to 
time, the path of the /noon is found to be the curve called the 
ellipse. 



* So used in Astronomy. Tn conic Sections, the eccentricity is the 
ratio between the semi-major axis and the distance above Stated, 



CHAPTER X. 

THE EARTH'S ORBIT. 

190. The sun's parallax. — Having found the parallax 
and distance of the moon, we inquire if the same method 
will find like quantities for the sun. Trial shows that the 
solar parallax, whatever it may be, is too small to be obtained 
reliably by direct observation, as in the former case. But 
we may obtain by indirect processes what we can not observe 
directly ; to understand these processes, and to be sure of our 
results, we follow somewhat the outline of discovery. The 
first point to be settled is the relation of the earth to the sun. 
Does the sun move about the earth annually, as it seems to 
do, or does the earth revolve about the sun ? 

191. The sun vastly larger than the earth. — We 

have said that the solar parallax can not be directly found, 
yet for many years our instruments have been so accurate, 
and our methods so reliable, that we can confidently deter- 
mine angular quantities of 20", 15", or considerably less. 
The parallax must therefore be less than the angle which we 
can confidently determine; certainly less than 20". Suppos- 
ing it to be 20", how large is the sun? The sun's parallax is 
equal to the apparent radius of the earth, as seen from the 
sun (178); the sun's apparent radius, as measured by the 
micrometer, averages 16' 2" = 962". As the real diameters 
of two objects which are equally distant from an observer, 
are in proportion to their apparent diameters, 

Sun's parallax : App. Rad, of S : : Dia. of E : Dia. of S; 

Or, 20" : 962" : : 1 : 48, nearly. 
(100) 



THE EARTH'S ANNUAL MOTION. 101 

Hence, if the sun's parallax is as small as 20", the sun's 
diameter must be 48 times the diameter of the earth. Since 
volumes are as the cubes of diameters (179), the bulk of the 
sun is at least 48 s , or 110,592 times the volume of the earth. 
But our assumed parallax is confessedly too large, hence our 
computed results fall far short of the truth; we may at least 
conclude that the sun is vastly larger than the earth. 



THE EARTH'S ANNUAL MOTION. 

192. The sun's motion may be only apparent. — 

It may be a result of the real motion of the earth. Let S 
be the sun; AB, a. path in which the earth moves about 




Fig. 67. 



the sun. When the earth is at A, the sun will be seen 
against the sky at M ; as the earth moves to B, the sun will 
seem to move to N, and so on to the place of beginning. 

193. The sun does not move. — It is more reasonable 
to believe that a small body moves about one which is vastly 
larger than itself, than that this large body should nunc 
about the smaller one. Since the apparent annual motion 
of the sun may be produced by the actual revolution o\ the 
earth about the sun, we conclude that it is the earth that 
moves, and that the sun is at rest. 



102 ELEMENTS OF ASTRONOMY. 

194. Velocities. — The real velocity of the earth in its 
path or orbit, is the number of miles which it passes over 
in a unit of time, as a day, or an hour. This amount we 
may not know until we find the radius of the orbit, or the 
distance of the earth from the sun. The angular velocity 
of the earth is the angle formed in a unit of time at the 
center about which the earth moves. The arc AB repre- 
sents the earth's real or linear velocity; the angle ASB, its 
angular velocity, and this angle is measured by the arc MN, 
which the sun appears to describe in a unit of time. 

195. The angular velocity is not a measure of 
the linear velocity, but is greater as the moving body is 
nearer the center about which it moves. A man walking in 
a circle around a post at a distance of ten feet, will move 
through half his orbit, or 180 , by walking about 31 feet; 
another, 20 feet from the center, would pass through only 
one fourth of his orbit, or 90 °, in walking the same distance. 
If the two men walk at the same rate, the angular velocity 
of the man at 10 feet is twice that of the man at 20 feet. 

196. Observations. — The sun's disc has been measured 
carefully, day by day, for every day in the year. Whatever 
the average distance from the earth to the sun may be, we 
may call it a unit ; the relative distances for each day are 
inversely as the breadths of the disc (182). 

With the transit-instrument and the astronomical clock, the 
amount of the sun's apparent motion in right ascension is 
found for each day (106). From this, the motion in longi- 
tude (119) may be determined, -either on the celestial globe 
(108), or by computation. The sun's motion in longitude is 
the measure of the earth's angular motion. From the two 
series of observations, a plan of the earth's orbit may be 
made, as in the case of the moon (184). 

197. Facts observed. — 1. The sun's greatest apparent 
diameter is measured on the 30th December, and is 32' 
36.4". The least occurs on the 1st July, and is 31' 31.8". 



THE EARTH'S ORBIT ELLIPTICAL. 103 

2. The sun's apparent motion in longitude on the 30th 
December is 61/ 11.1"; on the 1st July, 57' 13. 1" . The 
earth is nearest the sun, and its angular velocity is greatest, 
while it is winter in the northern hemisphere. 



THE EARTH'S ORBIT ELLIPTICAL. 

198. Ancient astronomers knew that the sun's apparent 
daily motion is not uniform. They accounted for the fact by 
supposing that the real velocity is uniform, but that it moves 
in a circular orbit whose center is not at the center of the 
earth. They supposed that the portion of the sun's path 
measured off in a day in June seemed smaller than the 
average, because it was farther away. If their suppositions 
were correct, the variation in the amount of the sun's daily 
motion should be in the same proportion as the variation in 
the breadth of the sun's disc for the same day. That is, 

32' 36.4": 31' 3i-8":: 61' n.l":57' 13.1" 
Or, 1956.4": 1891.8":: 3671.1": 3433-1" 

But this is not a true proportion, therefore the orbit is not 
a circle. 

199. The ratio of angular motion. — The ratio of 
greatest and least distances is equal to the ratio of greatest 
and least discs (182), and is, therefore, 

3 2 ' 3^-4 r/ _ i95 6 4 _ _ 

31' 31.8" " I89I8" 1 - 0341 ' 

The ratio of greatest and least angular motion is 
— ; 7, = —- 1. 069? 4. 

57' 13. 1" 3433i 

Squaring the first ratio, we have 1.06936-}-. nearly the 
same as the second ratio; if our divisions are carried to a 



io4 



ELEMENTS OF ASTRONOMY. 



greater number of places of decimals, the difference is still 
less. Hence, 



ist ang. vel. : 2d ang. vel. 



3671. 1 :3433-! 
1956.4 2 : 1891.8 2 
2d Dis 2 : ist Dis 2 or 



The angular motion af the earth is inversely proportional to 
the squa?'e of the distance from the sun. 

But this is a condition which would result from an ellip- 
tical orbit, when the real motion is inversely proportional to 
the distance. 

200. The ratio of real motion. — Let ABDE be the 

earth's orbit. Suppose it to be an ellipse (187) with the sun 

at one of the foci. As the 
earth moves from A to B, 
the radius vector SA takes 
the position SB, and is 
said to describe the space 
ASB. The area of this 
space, considered as a tri- 
angle, is the product of 
AB X }4 SC (Geom. 3 86.) 
Kepler discovered that 
the areas described by 
the radius vector in equal 
times, are equal. That is, 

if the time in which the earth passes from A to B equals the 

time in which it passes from D to E, the area ASB equals 

the area DSE, or, 

ABX }4 SC=DEX y 2 SE. 

Multiply the equation by 2, to remove fractions, and 
change to a proportion; 

AB : DE : : SE : SC, or, 




Fig. 68. 



KEPLER'S LAWS. 105 

The real motion of the earth is inversely proportional to the 
distance from the sun. 

KEPLER'S LAWS. 

201. About the year 1601, the German philosopher, Kep- 
ler, having adopted the Copernican theory of the solar system, 
began to study the planetary orbits. He found that they are 
not circular, as had been supposed. He then invented 
various hypotheses, and tested each in turn by comparing the 
position of the planet Mars, as computed by his hypothesis, 
with its real place as observed. Thus he devised and aban- 
doned nineteen before he found one which would answer the 
test during a planet's entire revolution. The successful hy- 
pothesis he announced to the world in his famous laws : 

First law. The path of each planet is an ellipse, having 
the sun in one focus. 

Second law. The velocity of each planet is such that its 
radius vector sweeps over equal spaces in equal times. 



THE LAWS OF FORCE AND MOTION. 

202. A body at rest can not put itself in motion : a body 
in motion can not stop itself, or in any way change either 
the direction or quantity of its motion. This quality of 
matter is called inertia. Force is whatever causes or impedes 
motion, or changes its direction. 

203. Compound motion.— Let a particle of matter. A 
(Fig. 69), be impelled by a force which, in a unit o\ time. 
will move it to B ; at the same instant, let the panicle be 
impelled by a second force, which, in the unit of time, will 
move it to C : in obedience to the two forces, the body will 
move to /), along the diagonal o( the parallelogram which 
has for two of its sides the lines .//>' and ./(.'. The line AD 



io6 



ELEMENTS OF ASTRONOMY. 




Fig. 69. 



is the resultant of the two forces. The body will continue 
to move in the direction of AD, and with the velocity of 

the first unit, until some 

AJi b other force changes the 

direction or the quantity 
of its motion. 

204. Curvilinear 
motion. — How will a 
body move, if impelled 
by two forces, one of 
which acts by a single 
impulse, the other acting continuously toward the same point? 
Let a body, A, constantly drawn toward a center, O, as by 
the attraction of gravitation, be moved by a single impulse, 
in the direction AC. Let the impulse be sufficient to move 
the body to C in a unit of time, while the radial force alone 
would move it to B. In the first unit of time, the body 
impelled by the two 

forces will describe the dr^= >^ 

resultant. AD, and will 

have an impulse which, 

in the next unit of time, 

will carry it to F, in AD 

prolonged, making DF 

equal to AD. But at D 

it again feels the radial 

force with an amount 

represented by DE; at 

the end of the second 

unit of time, it is at G ; 

in like manner, it may be traced to K, N, R, etc. But 

the radial force is said to be continuous, that is, acting at 

intervals which are infinitely short; hence the lines AC, AB, 

and AD, etc. , while they keep the same ratios to each other, 

become infinitely small, and the broken line ADGKN, etc., 

becomes a curved line passing through the same points. 




Fig. 70. 



THE LAWS OF FORCE AND MOTION. 107 

Hence a body impelled by two forces, the one acting con- 
tinuously toward the same point, and the other by a single 
impulse, describes a regular curve about the given point as 
a focus. If the curve is such that it returns into itself, it 
may be shown that it is an ellipse, or a circle, which is one 
variety of an ellipse (188). In passing along the curve 
ADGK, the rad. vec. AO describes equal areas in equal limes 
(App. IV). 

205. Application. — The laws of curvilinear motion apply 
to a stone thrown from the hand, to a drop of water spout- 
ing from a tube, to a cannon-ball, to the moon .revolving 
about the earth, or to the earth revolving about the sun. 
In the first cases, the tangential force is the force of projec- 
tion given to the stone, drop, or cannon-ball; the radial force 
is the attraction of the earth. In the last cases, the radial 
force is still attraction of the earth or sun, and the tangen- 
tial force is the impulse which the moon or the earth pos- 
sesses as the result of its precedent motion. In any case, 
the motion continues in an elliptical orbit forever, if no 
other force intervenes to modify or destroy. 

206. Effect of modification of forces. — The shape 
of the curve is determined by the relation between the two 
forces. If the tangential force were weakened, the body 
would describe a smaller and more flattened ellipse; if that 
force were quite destroyed, the radial force would at once 
take the body in a straight line to the attracting body. 
If the radial force were weakened, the ellipse would be 
made larger; and if destroyed, the body would obex the 
tangential force, moving away from the point ol tangency 
in a straight line, which it would continue to follow until 
it came within the influence of some other modifying force. 

207. The present adjustment of the two forces is necessary 
to retain the earth in its present orbit. It is not true, as 
many suppose, that the slightest diminution ot the projectile 

force would plunge the earth inward to the sun; it would 



108 ELEMENTS OF ASTRONOMY. 

merely cause the earth to adopt a new path, which would 
thenceforth be as stable as the present one, until some new 
disturbance should again change it. Of course, a constant 
diminution would produce constant change, which would 
in the end involve destruction. 

208. The eccentricity (187) of the earth's orbit. — 

Call the mean distance of the sun, 1; the least distance x, 
and the greatest distance y. Then, 

x -\-y = 2. 

(194-8) 



But 


x : y : 


: 1891.8 : 1956.4; 


Whence, 


x = 


= 0.9833; y— 1. 0168, 



The eccentricity of an ellipse is found by subtracting the 
least from the mean radius. The eccentricity of the earth's 
orbit is, therefore, 1 — -9833 = .0167; about .017 of the 
mean distance. 

209. The earth's orbit nearly circular. — If a plan 
of the earth's orbit were drawn upon a floor, using a mean 
radius of 10 feet, the eccentricity would be about 2 inches, 
and the breadth of the ellipse would be about .03 of an inch 
less than the length. It would require a microscope to dis- 
tinguish the curve of this ellipse from that of a circle drawn 
on the same major axis. 

210. Perihelion and aphelion. — The perihelion* is the 
point in the earth's orbit nearest the sun. A similar point in 
the moon's orbit is called perigee. The point of aphelion is 
that farthest from the sun; the corresponding point in the 
moon's orbit, farthest from the earth, is called apogee. The 
line which joins the points of perihelion and aphelion, or 
of perigee and apogee, is the line of apsides. It is the only 
diameter (187) of the orbit which passes through the sun's 



* Ilepi, peri, near ; airo, apo, away from ; qfaog-, helios, the sun ; yq, 
ge, the earth ; aipig, apsis, plural apsides, the joining. 



THE CHANGE OF SEASONS. IOQ 

center, and therefore the only line passing through the sun 
which divides the ellipse equally. The earth is at perihelion 
about January 1; at aphelion, about July 1. 



THE CHANGE OF SEASONS. 

211. The center of the heavens. — Our ideas must 
expand with our knowledge. At first we found the center 
of the sky in ourselves (1); then we conceived of it at the 
center of the earth (6) ; we must now seek it in that vastly 
larger body about which the earth revolves, the sun. We 
must think of the earth as of a body from which we are 
removed, and in which we have no immediate personal 
interest ; as part of a vast machine, a body making an annual 
circuit about a remote center, in a nearly circular path, of 
whose diameter we as yet know only that it is very large. 
Yet, as compared with even this large diameter, the radius 
of the sky is infinitely larger. It is so large that, although 
the earth is moved in six months from one side of its large 
orbit to the other, the axis of the earth points without vari- 
ation to the same place on the surface of the sky; and the 
plane of the equator, when extended outward from any posi- 
tion in the annual path, cuts the sky invariably in the same 
equinoctial line. 

212. Astronomical apparatus and diagrams always fail to 
represent astronomical proportions. Either the bodies arc 
too small to be seen, or the curves arc too large to be put 
on paper. But they may exhibit the relations of parts , and 
for that purpose Fig. 71 is inserted. The earth is repre- 
sented as passing round the sun in an elliptical orbit, the 
sun being in one of the foci (201). The plane oi the earth's 
orbit extended cuts the surface of the sky in a great circle, 
Which is the apparent annual path o\ the sun. the ecliptic 
(5cS). The plane o( the earth's equator extended cuts the 
sky in the equinoctial ( v ^0. These two great circles bisect 



no 



ELEMENTS OF ASTRONOMY. 



each other (Geom. 748), and the line common to the planes 
of both passes through the sun and through the equinoxes 
(55). From the time of the autumnal equinox, in September, 




S.POLE 



POLE OF ECLIPTIC 
Fig. 71. 



to the vernal equinox, in March, the sun appears in the 
southern sky; during the remainder of the circuit, he appears 
in the northern sky. 

213. The sun longest in the northern sky. — The 
earth's radius vector is least in December (197). Hence the 
line which joins the equinoxes divides the orbit into two 
unequal parts, the less being that traversed in our winter. 



POSITION OF AXIS. 1 1 1 

But the times are as the areas described by the radius vector 
(201); hence the earth passes more quickly over the northern 
or smallest part of its orbit, and the sun seems to pass more 
quickly over the opposite southern portion of the ecliptic. 
Although the sun is north of the equinoctial more than half 
the days of the year, his distance from the earth is more 
than the average; the aggregate amount of heat received by 
the northern hemisphere is therefore no greater than that 
received by the southern. 



POSITION OF AXIS. 

214. The change of seasons can not, therefore, be 
due to the difference of the earth's distance from the sun at 
different times of the year. It is caused by the annual revo- 
lution of the earth, combined with the position of the earth's 
axis as related to the plane of its orbit. 

215. If the earth's axis were perpendicular to the 

plane of its orbit, there could be no change of seasons. The 
equinoctial would coincide with the ecliptic; the sun would 
be vertical during all the year at the equator, and would 
shine from pole to pole. Days would be of uniform length; 
the meridian altitudes of the sun at any place of observation 
would always be the same; the heat received by any part 
of the earth would only vary from day to day, in accordance 
with the varying distance from the earth to the sun. Alter- 
nations of heat and cold, summer and winter, seed-time and 
harvest, would cease, and the productiveness of the earth 
would be greatly diminished, or destroyed. 

216. If the earth's axis lay in the plane of its orbit. 
and, as now, should point constantly in one direction, the 
changes would be those we now observe, but vastly exag 
gerated. The equinoctial would be at right angles with the 

ecliptic; the sun would be vertical in turn over every part 



112 ELEMENTS OF ASTRONOMY. 

of the earth. At one season he would shine directly on the 
north pole, and his scorching rays, pouring down day after 
day, with no intervening night, would produce a degree of 
heat more intense than any which the earth now knows. 
Six months later the entire northern hemisphere, to the very 
equator, would be plunged into continuous night, while the 
cold would be as intense as the heat had been. No part of 
the earth would be free from these extreme vicissitudes of 
heat and cold, and no life, vegetable or animal, such as now 
exists, could endure such changes. 

217. The position of the axis. — The ecliptic makes 
with the equinoctial an angle of 23 ° 27' (58). The axis of 
the earth is, therefore, inclined from a perpendicular by the 
same amount, or makes an angle with the plane of the ecliptic 
of 66° 33'. The axis is always turned toward the same point 
of the far distant sky. It is always parallel to itself. 

DAY CIRCLE. 

218. Suppose a plane to pass through the center of the 
earth, perpendicular to the direction of sunlight. It will 
divide the earth into two hemispheres, one turned toward the 
sun, and illuminated, the other turned away, and in darkness. 

On one side of the circle is day, on 
the other side, night; we may call it 
the day-and-night circle, or, briefly, 
the day circle. This circle may be 
conceived to accompany the earth 
in its annual revolution, the light side 
always toward the sun. The earth 
may be conceived to rotate beneath, 
or within this circle ; when any point 
passes from the dark to the bright 
side, the sun rises for that point ; when the same point passes 
again under the circle, the sun sets. A globe fitted with a 
circle of this kind is very convenient for illustration. 




DA Y CIRCLE. 



"3 



219. The Tropic of Cancer. — At the summer solstice 
(56), on the 20th of June, the earth is near the southern point 
of its orbit, its north pole inclines toward the sun, and the 
sun's rays fall vertically 23^ ° north of the equator. The 
sun's northern declination has been increasing day by day 
(136) up to this time, and from this day will decrease; the 




Fig. 73- 

sun seems to turn and go back to the equator. The parallel 
of 2314 is called a tropic* and, because the sun is in that 
part of the ecliptic called the sign Cancer, it is the Tropic 
of Cancer. It marks the greatest distance north of the 
equator at which the sun's rays are vertical on any day oi 
the year. 

220. The Polar Circle. — The day circle, being always 
perpendicular to the plane of the earth's orbit, is 23j£° 



*T(K>n-/A<ic, tropt&os, turning 

Ast.— 8. 



H4 



ELEMENTS OE ASTRONOMY. 



from either pole. A person 23^° from the north pole may 
make an entire revolution about the pole, as the earth rotates, 
without passing beyond the day circle; for him the sun does 
not set. The circle of latitude farthest from the pole at which 
the sun does not set on the longest day of the year is a polar 







wm^m-: 












" : "" ::: : .!■■ 


MBS55 


2^^^^ 


mB?f\ :■.': '.' ' ; ,-:■ 












^^mlmltmlnl'i'nii ■ ■ 


'«■*>&*:'- ■ 


-c * - ^ \iB 111 If 


HES'S-'','i{i»'-L _: 


^F/ 1 


■ 


m Fij -* 


^v 




p|\ll» l 1 " ''.V?' 


Hr\ 


\^i 


iff, 






■fe 


Ki^M^ 






:■':' . . 


Bk - ""~ 


i-SB-" 1 '^" "—-i ' il rii^iSv? 


illjijjii'h ■ 


\^k\ '- \ ~~~~~~~^~/y~~: 








i'l'ii'ifi' l 1 ' 'I 


!|j|:, , ..,„: 


^^L^"^ 


i\St'| 


SSI 


^^^. 


— "i ' T.nHiiij^H|^H 


HWpP ~-~ 


^k. 


/^j WHtt 


^Bi^X -.. 




fljil'lj'; 












w"^ w . -- 



Fig. 74- 



«>r/<?. On the same day, a person 23^° from the south pole 
may make one entire revolution about the pole without see- 
ing the sun rise. 

221. The season. — At this time, in the northern hemis- 
phere, the sun's rays fall most directly, and the days are 
longer than the nights; heat is most abundant, and the season 
is summer. In the southern hemisphere, the sun's rays fall 
obliquely; the nights are longer than the days; heat is least 
abundant, and the season is winter. 

222. The winter solstice. — On the 22d of December, 
the earth reaches the northern place in its orbit, the sun has 



DAY CIRCLE. 



its greatest southern declination, and all the preceding con- 
ditions are reversed. The sun's rays are vertical 23^° south 
of the equator, at the Tropic of Capricorn. The day circle is 
removed 23^° beyond the south pole, forming the south 
polar circle, at which the sun for that day does not set ; at 
the north polar circle, the sun does not rise. It is summer 
in the southern hemisphere, winter in the northern. 

As both the summer and the winter solstice find summer 
on some part of the world, it might be better to call the first 
the northern, the second the southern, solstice. 

The north polar circle is also called the Arctic circle; the 
south polar circle, the Antarctic circle. 

223. At the equinoxes (55), the earth's axis is inclined 
neither toward nor from the sun. The day circle passes 
through the poles; the sun is vertical over the equator; the 
day is equal to the night; the sun's rays are equally oblique 
in each hemisphere. It is spring on that side of the equator 
toward which the sun is 

moving; autumn, on that 
side from which he is 
departing. 

224. Zones. — The 

tropics and polar circles 

divide the earth's surface 

into five belts, called 

zones. The torrid zone 

lies on either side of the 

equator, between the 

tropics ; it includes all 

that part of the earth on 

which the sun's rays arc 

at any time vertical. The frigid '.ones lie between the polar 

circles and the poles; they include those portions of the 

earth on which the sun does not shine on some day o( the 

year. The temperate zones lie between the tropics and the 




F'g- 75- 



n6 



ELEMENTS OF ASTRONOMY. 



polar circles; in these parts of the earth, the sun's rays are 
never vertical, and from them the sunlight is never excluded 
during a whole day. 

The breadth of the torrid zone, and of each frigid zone, 
is 47 ; each temperate zone is 43 ° wide. 



SUMMER HEAT. 

225. First cause of summer heat. — In summer the 
sun's rays are most nearly perpendicular to the earth's sur- 
face. The heat which falls perpendicularly on the surface 



f 




N 




— 


/- — \^ — yt— 


— — — — — 


X^ X \T = := ~ 


~- 


: — 








=*< 


X^ "^^ 


- SOLAR-HEAT— 


\- 


^ 




~ ~~ — — — ~_~ — 








— — — 






/!>s 




— 


— . 



Fig. 76. 



MN is distributed over a space smaller than the surface 
MQ, to which the same heat comes obliquely; the quantity 
received by a unit of surface at MN, is, therefore, greater 
than the quantity received by a like unit at MQ. 

226. Second Cause, — The earth constantly gives out 
heat by radiation; it receives solar heat at any place only 
when the sun is above the horizon of that place. The heat 
received during twenty-four hours is greater as the duration 
of sunshine is greater; hence, any place on the earth receives 
most heat during the long days of summer, and least during 
the short days of winter. When the heat received during 
twenty-four hours is more than that radiated during the same 
time, the place becomes gradually warmer ; when the heat is 
less than that radiated, it becomes cooler. 



SIGNS OF THE ECLIPTIC. 117 

227. The maximum of heat is not at the time of the 
summer solstice. At that time, the sun's rays are most 
nearly vertical in the northern hemisphere; the daily income 
of heat is largest; and, although the daily expenditure by 
radiation is largest, their difference, or the net increase for 
one day, is also largest. On succeeding days, the income, 
though not as great for one day, is still more than the ex- 
penditure, and the aggregate increases. This will continue 
until the maximum of heat for the season is reached, when 
the loss becomes equal to the gain by day, and begins to 
exceed it. The maximum of heat occurs when the sun's 
declination after the solstice is about 12 north; the maxi- 
mum of cold, when the declination is 12 south. Hence, 
the heat of summer begins to decrease about the 20th of 
August; the cold of winter abates soon after the 16th of 
February. 

For like reasons, the warmest part of the day is about 
2 o'clock p. m. ; the coldest time of night is shortly be- 
fore sunrise. 

228. In the southern hemisphere, all these results are 
reversed. It must be remembered that the reasoning ap- 
plies to the hemispheres as wholes, leaving out of consid- 
eration the modifying influences of oceans, continental forms, 
and mountain ranges. 



SIGNS OF THE ECLIPTIC. 

229. In the early days of astronomy, the ecliptic was 
divided into twelve parts, of 30 each, called signs; each 
sign was named from the group o( stars which was most 
prominent near it. The signs in order, beginning at the 
vernal equinox, were named Aries, Taurus, Gemini; Cancer. 
Leo, Virgo; Libra, Scorpio, Sagittarius; Capricornus, Aqua 
rius, and Pisces. The vernal equinox was at the first point 



n8 



ELEMENTS OF ASTRONOMY. 



in Aries, and was indicated by the symbol c f. The equi- 
noxes move westward along the ecliptic about 50" annually; 
this motion is called the precession of the equinoxes (App. V). 
The vernal equinox is now in the constellation Pisces; but, 
as the names of the signs remain unchanged, it is still the 
first point of the sign Aries. 

230. The length of the seasons. — The sun is said to 
enter a certain sign when the opposite sign comes to the 
meridian at midnight. The sun enters Aries at the vernal 



VERNAL EQUINOX 

MCH 20 V 




AUTUMNAL EQUINOX 
SEP 22 



Fig. 77. 



equinox; Cancer, at the summer solstice; Libra, at the 
autumnal equinox; Capricornus, at the winter solstice. But 
the motion of the earth over different parts of its orbit is not 
uniform (200); hence the apparent motion of the sun among 
the signs varies, and the seasons are of unequal length. 



EQUATION OF TIME. 119 

From Aries to Cancer, Spring, 92.9 days 1 

" Cancer to Libra, Summer, 93.6 " J ' 2 

" Libra to Capricornus, Autumn, 89.75 " 



Capricornus to Aries, Winter, 



78^ 



Spring and summer are together 7^ days longer than 
autumn and winter. 

231. Gradual changes in the length of seasons. — 

The line of apsides (210) moves slowly to the eastward, 
about 12" a year; the equinoxes move westward about 50" 
annually; the distance between perihelion and vernal equinox 
increases, therefore, about 62", or more than 1/ yearly. 
Perihelion is* in the nth degree of Cancer, in longitude 
ioo° 56'; about 60 X 100 = 6000 years ago, perihelion must 
have coincided with vernal equinox; spring was shorter than 
summer; but spring and summer were together equal to 
autumn and winter. About 11,000 years since, perihelion 
was near summer solstice; the earth being nearest the sun in 
June, both summer's heat and winter's cold must have been 
more intense than now, in the northern hemisphere. 

232. It is ascertained that the eccentricity (208) of the 
earth's orbit is diminishing gradually, the curve becoming 
more nearly circular. Leverrier estimates that 80,000 years 
ago the eccentricity must have been about three times the 
present amount, and that the solar heat in winter was so 
reduced by this cause, that the average winter temperature. 
instead of 39 F., as now, was between 6° and 23 below 
the freezing point. 



EQUATION OF TIME. 

233. Definition. — In algebra, an equation is an expression 
of the equality of two quantities. In astronomy, m\ equation 



Jan. 1. 1SS5. 



120 



ELEMENTS OF ASTRONOMY. 



is something which must be added to, or subtracted from, 
another quantity to bring it to a definite standard. It does 
not show that two quantities are equal, but rather what must 
be applied to one to make it equal the other. This use of 
the word may be illustrated by quotations of bank stock. If 
a share whose par value is $100 is sold for $98, the equation 
is $2, as that amount added to the price obtained will restore 
the par, or standard, value. If the same share sells for $104, 
the equation is — $4, for the same reason. 

234. Sidereal time has no equation, because the length 
of a sidereal day is invariably 23 h. 56 m. 4.09 sec. mean 
solar time (100). 




Fig. 78. 



235. Circumstances which would give no equation 
of solar time. — 1. If the sun appeared stationary in the 
heavens like a star, solar time would not differ from side- 
real time. 



EQUATION OF TIME. 121 

2. When the meridian of a place has come, by the rota- 
tion of the earth, to the place on the sky which it had at 
that time on the preceding day, the sun is no longer there, 
but has moved eastward, and the meridian must go on farther 
to overtake the sun. This is the apparent statement; the 
fact is, that the forward motion of the earth in its orbit has 
to be provided for by an equal movement of the meridian. 
During the day, the earth has moved in its orbit from O to 
O '. As the meridian comes to the position A, parallel to its 
position of the day before, it has made a sidereal revolution, 
since it points to the same place on the sky, but it must go on 
to the line O'S, to be opposite the sun. 

If the sun's motion among the stars were uniform, and were 
on the equinoctial, so that his daily change in right ascension 
were the same, there would be no equation of time. The 
solar day would be equal to the invariable sidereal day, in- 
creased by the uniform time required for the meridian to 
overtake the sun in right ascension. 

236. Mean solar time. — In four sidereal years there are 
very nearly 1461 days, or in one year 365^ days. A clock 
which has indicated 365^ days, of 24 hours each, in one 
year, has kept mean solar time (97). Twenty-four hours by 
this clock is a mean solar day. At certain times in the year, 
the time from noon to noon is about 8 seconds less than 24 
hours of mean solar time, and at other times about 24 seconds 
more. These differences accumulating day by day soon 
amount to an aggregate which is considerable. 

237. Equation of time.- -At 12 by the clock, the sun 
may have already passed the meridian, and is said to be fast 
of the clock ; it may not yet have come to the meridian, and 
is slow of the (-lock. 'Hie difference in time between ap- 
parent noon, as shown by the passage o( the sun over the 
meridian, and mean noon, as shown by the clock, on any 
day of the year, is the equation of time for that daw 



122 



ELEMENTS OF ASTRONOMY. 



CAUSES OF EQUATION. 

238. The causes which produce this variation in time 
are two: 

1. The unequal apparent motion of the sun on the 
ecliptic, caused by the unequal real motion of the earth 
in its orbit. 

2. The variable inclination of this motion from day to day 
to the equinoctial. 



e\e' <44- 



SUNIN 
>?tf T* JAN 




11 

'SUN IN DEC. 



239. First cause. — The earth's angular motion (194) is 
fastest when the earth is nearest the sun; that is, from Sep- 
tember to March, the greatest rate being on the 1st of Jan- 
uary. On that day, the earth makes more than its average 
angular progress, and therefore the sun makes more than his 
average apparent day's journey on the ecliptic. Hence, 
when the meridian is about to pass the sun on the next day, 
it finds that the sun has moved to the eastward of his position 
on the day before by an amount greater than the average, 



CAUSES OF EQUATION. 



123 



and, therefore, more time will be required for the meridian 
to overtake him. The sun is, accordingly, slow of the clock 
about 8 seconds on this account. The same result occurs on 
the next day, and the sun is now 16 seconds slow. The 
difference will continue to increase daily until soon after the 
vernal equinox, when the earth moves at its average rate. 

240. After equinox. — From the vernal equinox until 
apogee, the rate of the earth's angular motion is less than 
the average, and is constantly decreasing; the daily easting 
of the sun diminishes at the same rate. The length of the 
solar day, although still more than 24 hours of mean solar 
time, becomes gradually less, until the accumulated difference 
is entirely lost on the 1st of July, and the sun and clock, so 
far as this cause is concerned, come together again. After 
July 1 st, the sun becomes fast of the clock, as the sun's daily 
motion is less, and the meridian comes up with the sun in 
less than the average time; the action of the preceding half 
year is reversed. 

241. Second cause. — Were the sun's motion in longitude 
uniform, there would still be an equation of time. Difference 
in time is caused by dif- 
ference in right ascension 
(106), but a uniform amount 
of motion in celestial longi- 
tude, produces a variable 
amount of motion in right 
ascension. Let AC repre- 
sent part of the equinoctial 
and BD a part of the ecliptic crossing the equinoctial at /•'. 
Suppose that in one day the sun has moved from /■' to D; 
his difference of right ascension will be EC, less than /•'/>. 
because the base oi~ a right-angled triangle is less than the 
hypotenuse. The sun is not so far to the east as his motion 
would indicate; the meridian overtakes him sooner, ami the 
day is shorter by this cause. The sun is fast of the clock. 




Fig. 80. 



124 ELEMENTS OE ASTRONOMY. 

At the solstices the path of the sun is nearly parallel to 

the equinoctial, but is removed from it 23^°. The right 

ascension AB being reckoned on 

UPTIC the equinoctial is more than the 

actual distance traversed by the 

sun; the sun's relative easting is 

increased; the day is longer; the 
^MMOBAL. sun is slow Qf the dock> 



Fig. 81. 242. The equation for the 

day is found by combining the 
results obtained for each cause separately. Thus, on April 
4, the sun is slow from the first cause 7 m. 40 sec. ; from 
the second, fast 4 m. 46 sec. ; the equation is, therefore, -\- 
(7 40) — (4 46) = -f (2 54); when the sun is on the merid- 
ian, the clock should show 2 minutes 54 seconds past twelve. 

243. Morning and afternoon unequal. — Sunrise and 
sunset are equally distant from apparent noon; hence, if 
mean noon is, say, 7 minutes later than apparent noon, the 
clock adds 7 minutes to the morning, and subtracts it from 
the afternoon; the morning is 14 minutes longest. Sunrise 
and sunset will be as much slow or fast of the clock as 
midday. 

244. Table of equation of time. — The values of the 
equation for each day in the year have been computed, and 
are arranged in a table at the end of the book. It is more 
important that a watch should agree with a recognized 
standard, than that it should be absolutely correct. It is 
useless, however, to attempt to regulate a watch by a sun- 
dial, or by a noon mark, without correction for equation of 
time. To say that a watch runs with the sun, is to say that 
it is a poor time-keeper. 

THE CALENDAR. 

245. The tropical year. — The sidereal year is the time 
occupied by the earth in passing once round its orbit, or 



THE CALENDAR. 1 25 

until it has brought the sun back to the same star in the 
heavens. Its length is 365 d. 6 h. 9 m. 9.6 sec. But the 
vernal equinox has a motion backward along the orbit, 
amounting to 50" of arc per annum; the earth, therefore, 
comes back to the vernal equinox a little sooner than to the 
precise place it started from a year before, as shown by the 
stars. The time required by the earth to return to the vernal 
equinox is called the tropical year; its length is 365 d. 5 h. 
48 m. 46.05 sec. This is the year employed in the calendar; 
it is 20 m. 23.55 sec - l ess than the sidereal year. 

The time required by the earth to return to perihelion is 
the anomalistic year. It is 365 d. 6 h. 13 m. 49.3 sec. It 
will be remembered that perihelion moves forward about 
12" annually (231); hence, its year must be longer than the 
sidereal year. 

246. The Julian Calendar. — For practical purposes, it 
is convenient to consider some number of whole days a 
year. The Greek year had at different times 354, 360, and 
365 days. The Roman year, under Numa, had 355 days. 
There was a continual discordance between the civil year 
and the astronomical year, which reached such a degree that 
the autumn festivals were celebrated in the spring, and those 
of harvest, in midwinter. An extra month, called Merce- 
donius, was added every second year. The length of this 
month was not fixed, but was arranged from time to time by 
the pontiffs, and this gave rise to serious corruption and 
fraud, interfering with the duration of office and the collec- 
tion of debts. 

In the year 46, B. c, Julius Caesar reformed the calendar. 
To restore the seasons to their proper months, he made that 
year contain 445 days. Assuming the astronomical year to 
De 3^5 V\ days, he made each fourth year to contain 300 
days; the remainder, 365. The added day was placed in 
the month o( February. The 24th of February, called sexto 
calendas, being the sixth before the calends, or 1st o( March, 
was celebrated in honor i^~ the expulsion o\ the kin^s; the 



126 ELEMENTS OF ASTRONOMY. 

additional day was placed next to this feast, and was called 
Bis-sexto-calendas, whence our name Bissextile. 

247. The Gregorian Calendar. — The astronomical 
year, as assumed by Caesar, was too long by 11 m. 13.95 sec, 
or about 3 days in 400 years. By the year a. d. 1582, the 
error had grown to 10 days. So many days had been 
wrongly reckoned into the years that were gone, and, there- 
fore, the dates were 10 days behind what they should have 
been. To correct this error, Pope Gregory XIII ordered 
that the 5th of October of that year should be called the 
15th, and the order was forthwith obeyed in all Roman 
Catholic countries. It was also arranged that three inter- 
calary days should be omitted in four centuries, or one in 
each centenary year except the fourth. Hence, the years 
which have 366 days are, first, those whose numbers are 
exactly divisible by 4, and not by 100; second, those whose 
numbers are divisible by 400, and not by 4000. 

The Gregorian calendar was introduced into England and 
her colonies in 1752, the error being then 11 days. Dates 
previous to the change are sometimes referred to as O. S., 
Old Style; occasionally, dates are given with reference to 
both styles. Washington's Birthday was February u / 22 ; the 
nth of February, O. S., or 2 2d of February, N. S. 

The Gregorian calendar is used in all Christian countries, 
except Russia. The error in the Julian calendar is now 
12 days. 



248. RECAPITULATION. 

As the sun's parallax must be less than 20", the sun is, in diameter 
more than 48 times, in volume more than 110,000 times, as large as 
the earth. Being so much larger, the sun must be at rest, rather than 
the earth. 

The earth's orbit, found from the apparent size and angular motion 
of the sun, is an ellipse. 



RE CAP/TULA TION. 1 2 7 

Kepler's Laws : 

First ; Each planet revolves about the sun in an elliptical orbit, 
the sun being at one focus. 

Second ; The velocity of a planet is such that the line drawn from 
the sun to the planet sweeps over equal areas in equal times. 

A single impulse of projection and a constant attraction toward a center 
are enough to cause motion along the curve of an ellipse. 

Change of seasons is due, not to the varying distance of the sun, but 
to the angle made by the earth 's axis with the plane of its orbit. 

Tropics are at the greatest distance from the equator at which the 
sun's rays fall vertically. 

Polar circles are at the greatest distance from the poles at which the 
sun does not set during twenty-pour hours once in a year. 

The heat at any place is greatest in summer, because the surface of 
the earth is then in position to receive the greatest number of heat- 
rays; and because more heat is received daily than is radiated. 

Equation of time is required on account of the variable apparent 
motion of the sun along the ecliptic, and the variable inclination of 
that motion to the equinoctial. 

In a Sidereal year, . ~\ f the same star. 

Anomalistic, I " " -s tne P er ^ ie ^ on ' 

Tropical or Calendar, \ ( the vernal equinox. 



CHAPTER XL 



PLANETARY MOTIONS. 



249. In the preceding chapters, we have learned: 

The sun's distance from the earth is very great; how 
great we can determine only when we know its horizontal 
parallax. 

The sun is very much larger than the earth. 

The distance from the earth to the sun is not uniform, 
but the variations in distance, and in both real and angular 
motion, are regular. 

The moon is comparatively near the earth; its distance is 
variable; its mean distance and the amount of its variations 
are known. In the sky it appears as large as the sun; in 
fact, it is smaller than the earth. 

250. Planets. — When a star does not pass the meridian 
at regular intervals of a star-day, we know that it has a 
motion of its own in the sky. Ancient astronomers recog- 
nized five such bodies, besides the sun and moon : they 
called them planets (117). They named them after their 
gods, Mercury, Venus, Mars, Jupiter, and Saturn. Modern 
astronomy has added many others to the list. 

Their motions are apparently irregular. Generally they 

move from day to day toward the east; sometimes they are 

stationary, and at times they move westward. The apparent 

motion of a planet toward the east is said to be direct; that 

toward the west is I'etrograde. 
(128) 



VENUS. 129 

251. The Zodiac. — When the successive positions of the 
planets are marked upon the celestial globe, they are found 
in very regular paths among the stars not far from the 
ecliptic. The ancients observed that these movements are 
included in a narrow belt extending eight degrees on either 
side of the ecliptic; this belt they called the Zodiac. The 
zodiac, like the ecliptic, was divided into 12 parts, called 
signs (229). 

VENUS. 

252. The evening and morning star. — At certain 
seasons, a brilliant star appears in the south-west soon after 
sunset; this star the Greeks called Hesperus; we call it the 
evening star. Gradually, night by night, it departs from the 
sun. When it has gone about 45 °, it remains for a few 
nights nearly stationary ; then it returns, and disappears. 

Soon after the departure of the evening star, a bright star 
is seen in the south-east, a little before sunrise. It is Lucifer, 
the morning star. Like the evening star, it goes from the sun 
about 45 , then returns and disappears. Thus, for more than 
3000 years, have the alternations of these stars been recorded ; 
they never appear on the same day, and are always seen on 
opposite sides of the sun. They are evidently the same 
body that revolves regularly about the sun: it is the planet 
Venus. 

253. Venus in the telescope. — The rays, which to the 

naked eye surround the star, vanish in the telescope, and we 
see a disc with phases like the moon. When near the sun, it 
shows first a small, round disc ; as it departs, the disc grows 
larger, but a portion seems to be removed from the side 
farthest from the sun; at the greatest distance, the bright part 
is a semicircle; while it returns, the disc grows narrower and 
larger, day by day, until just before it disappears it shows .1 
fine narrow crescent, the points or horns turned away from 

the sun. The morning star reverses these appearances. 

Asr. — 9. 



i 3 o 



ELEMENTS OF ASTRONOMY. 



There is first the fine crescent, as if cut from a large circle, 
lastly, the full circle of small diameter. 




Fig. 82. 



254. Transits. — When the planet is near the sun, it 
vanishes in the bright sunshine; sometimes between its 

disappearance as even- 
ing star, and its re- 
appearance as morning 
star, it is seen to cross 
the sun's disc during 
the day, as a round, 
black spot. This pas- 
sage before the sun is 
called a transit. 

255. Mercury. — 

Another planet, still 
nearer the sun, exhib- 
its the same series of 
changes. It appears in 
the evening, soon after 
sunset, at a distance of about 25 , and vanishes; it afterward 
appears again in the morning; it exhibits phases, and some- 




Fig. 83.— Transits of Mercury. 



MARS. 131 

times makes a transit. Its variations are not as great as 
those of Venus, and its changes are completed in less time: 
its name is Mercury. 

256. Inferences. — All the movements of these bodies 
will be easily understood, if we suppose that these planets 
are opaque bodies, which reflect light from the sun and re- 
volve in regular orbits about it. The orbit of Mercury is 
within that of Venus, and both are within the orbit of the 
earth. Tycho Brahe believed that they revolve about the 
sun, but thought that they accompany the sun in its revolu- 
tion about the earth. 

MARS. 

257. A bright red star, called Mars, appears at times in 
the east about sunset, crossing the meridian near midnight. 
He is in the part of the sky opposite to the sun. In a few 
months he journeys among the stars until he sets with the 
sun; then he continues his round until he appears again in 
the east at sunset. He is never seen to pass between the sun 
and the earth. In the telescope, he never shows the fine 
crescent which is shown by Mercury and Venus. Although 
in the same part of the sky, he is evidently beyond the sun, 
and his path encircles both the earth and the sun. His 
diameter is greatest when he is opposite the sun; it is then 
about 23"; it is least when in the same quarter of the sky 
as the sun ; it is then about 4". But his distance from the 
earth must vary inversely as his apparent diameter (182), and 
therefore his distance when he is nearest is to his distance 
when most remote as 4 to 23. 'The sun is evidently much 
nearer than the earth to the (-enter of his orbit; it is more 
likely, moreover, that he revolves about the sun. than about 
the earth, as the sun is by far the larger and more powerful 
of the two. 

258. Retrograde motion. The general motion o( all 
the planets among the stars is eastward, or direct ; when 



132 



ELEMENTS OF ASTRONOMY. 



they come into the quarter of the sky which is opposite the 
sun, their motion is westward, or retrograde. If the earth 
were the center of their motions, we must suppose that the 
planets actually return and retrace part of their course. 
Ancient astronomers recognized this fact, and evaded this 
conclusion by supposing that the planets move about the sun, 
and with it about the earth, describing very complicated 
curves, called epicycles, such as might be made by a nail in 
the rim of a wheel as it rolls about the rim of another wheel. 
This opinion was generally adopted by philosophers, and 
Milton refers to it when he speaks of the heavens as 

"With centric and eccentric scribbled o'er, 
Cycle and epicycle, orb in orb." 




Fig. 84. 



THE C0PERN1CAN SYSTEM. 



J 33 



Figure 84 shows the supposed path of Mars, from 1708 
to 1723, as drawn by Cassini. The earth is supposed to 
be in the center, while the dotted line shows the path of 
the sun. 



THE COPERNICAN SYSTEM. 



259. Aristarchus of Samos, 280 b. c, and Cleanthes of 
Assos, 260 b. c, suggested that the earth with the other 
planets revolves about the sun, but their opinions were so 
different from the doctrines commonly held, that they were 



SUP. CONJUNCTION 




QUADRATURE 



OPPOSITION 
Fig. 85. 



accused of impiety. In 1543, the ideas ol~ the Pythagorean 
philosopher, Philolaus, wore revived by Copernicus, a Prus- 
sian. About sixty years later, Galileo was forced to retract 
his statement of the same truths. It remained for Kepler, 
in 1619, to establish the true theory of the planetary system, 
by discovering that the planets, in their motions, obey the 
laws which bear his name. 



134 



ELEMENTS OF ASTRONOMY. 



260. The true solar system. — Since the discoveries 
of Kepler, the sun has been recognized as the central body 
about which the planets revolve in elliptical orbits, nearly 
circular. The planets, in their order from the sun, are Mer- 
cury, Venus, the Earth, Mars, the Minor Planets, Jupiter, 
Saturn, Uranus, Neptune. Those within the orbit of the 
earth, Mercury and Venus, are inferior planets. Those with- 
out the orbit of the earth are superior planets. 




Fig. 86. 



261. Conjunction and opposition. — Two bodies are 
in conjunction in the sky (Fig. 85), when they have the 
same celestial longitude (119). The bodies in conjunction 
are evidently on the same side of the earth. If they are 
the sun and a planet, the conjunction is called inferior 
when the planet is between the earth and the sun; superior, 
when the planet is beyond the sun. Two bodies are in 



APPARENT MOTION EXPLAINED. 



*35 



opposition when their difference in celestial longitude is 180 ; 
they are in opposite parts of the sky, and in opposite direc- 
tions from the earth. 

A planet is in quadrature when its position in the heavens 
is 90 from the sun. The positions, conjunction, opposition, 
and quadrature, are sometimes called the aspects of the 
planets. The astrologers added several others to the list. 



APPARENT MOTION EXPLAINED. 

262. Inferior planets. — Let the outer circle in figure 
86 represent the sky, and the inner circles the paths of 




Venus and the earth, their successive positions being shown 
by the figures 1, 2, 3, When the two bodies are in the 
places marked 1, Venus appears at .-•' on the sk\ ; when 



136 ELEMENTS OF ASTRONOMY. 

they have moved to the places marked 2, Venus seems to 
have gone back to v 2 , or to have retrograded; when they are 
at 3, Venus appears to have gone forward to v z , and so on. 
Evidently, at some place between V 2 and V s , Venus moves 
a little way on a line directly away from the earth, and 
therefore she seems stationary on the sky. 

263. Superior planets. — Let the inner circles of figure 
87 now represent the orbits of the earth and Mars, the posi- 
tions being shown as before. While the earth and Mars are 
moving regularly to the positions 2, 3, and 4, Mars appears 
in the sky to go forward to m 2 , backward to ;;z 3 , and, 
finally, forward to ;;/ 4 . In the vicinity of m 2 and m s , there 
are places where the planet seems to be at rest, when 
changing its apparent motion from direct to retrograde, 
and back again. Thus the Copernican theory of the solar 
system explains easily and simply all the apparently erratic 
and complicated motions of the planets. 



THE TIMES OF THE PLANETARY REVOLUTIONS. 

264. Sidereal revolution. — The time occupied by a 
planet in passing once round the sun is the time of its sidereal 
revolution. If seen from the center of the sun, the planet 
would return in that time from one star on the sky to the 
same star again. A sidereal revolution can not be observed 
from the earth, since the earth is in motion; its length can 
be found only by computation. 

265. Synodic revolution. — A synodic revolution is 
completed when the three bodies, — the planet, the earth, 
and the sun, — come again into the same relative position, 
as, into conjunction or opposition. Let the circles repre- 
sent the orbits of Jupiter and the earth. Suppose the planets 
are in conjunction on the line SEJ, starting evenly together 
in their race about the sun. When the earth has completed 



TIMES OF PLANETARY REVOLUTIONS. 



137 



one revolution, and has come back to the line S/, Jupiter 
is not there, and the earth overtakes him somewhat farther 
on, in the line SE'J'. The two bodies have completed 
one synodic* revolution; the time is that between two suc- 
cessive conjunctions of the same bodies. 




266. To find the time of a sidereal revolution of 
Jupiter. — During one synodic revolution, the earth lias 
passed over its entire orbit and the arc EE\ opposite the 
angle ESFJ ; Jupiter has passed over the arc //'. also oppo- 
site the angle ESFJ, and therefore containing- as mam- 
degrees as EFJ . By observation, the time o\ Jupiter's 
synodic revolution is 398.8 days. The earth went from E 
to E again in 365.26 days, and therefore passed the space 
EE' in 398.8 — 365.26. 33.54 days. As the earth tie 
scribes 360 in 365.26 days, it passes 360 : 365. 26, or 
0.9856 , in one day ; and as it had been moving 33.54 days 



*2(>vo(Jorj sunodos, owning togeth< 



He 



modi an assemblai 



138 ELEMENTS OF ASTRONOMY. 

at that rate, it had passed over 33.54 X 0.9856 = 33.06 = 
the angle described by Jupiter in one synodic revolution. 
But evidently, 

Ang. of Syn. Revolution : Whole Revolution : : 
Time of Syn. Rev. : Time of Sidereal Rev. 
33.06 : 360 : : 398.8 days : 4342 days. 

Hence, Jupiter's year equals about 4342 of our days, or 
nearly 12 of our years. 

267. Sidereal revolution of Venus. — This is found 
as before, except that Venus is the inner of the two planets. 
The time of synodic revolution is 584 days. In this time, 
the earth has described 584 X 0.9856 = 575. 6°. But 
Venus has made one circuit more than the earth, and has, 
therefore, described 575. 6° -f 360° =935.6°, in 584 days. 
Then, as before, 

935. 6° : 360° :: 584 days : 224.7 days, 

the length of Venus' s year. 

A table of synodic revolutions will be found on page 141, 
and pupils should find the length of year for the other 
planets from the data there given. The results will not agree 
strictly with those of the table; first, because they are found 
as if the orbits were circular, and the motions uniform; 
second, the data are in days, neglecting fractions of a day. 

268. A more accurate method. — On the 7th of No- 
vember, 1 63 1, M. Cassini observed a transit of Mercury; 
the time of conjunction was 7 h. 50 m., a. m., mean time, at 
Paris, and the longitude of Mercury, 44° 41' 35". Another 
conjunction was observed in 1723, November 9, at 5 h. 29 
m., p. m., the longitude being 46° 47' 20". The time which 
had elapsed was 92 y. 2 d. 9 h. 39 m. Adding 22 days for 
the leap-years in that time, and reducing, we have 33604.402 
days. During that time, Mercury had made 382 revolutions 
and 2 5' 45" more. In 33604.402 days, Mercury had de- 
scribed 137522.09583 degrees, or 4.09234 degrees in one 



DISTANCE OF PLANETS FROM THE SUN 



139 



day. This, then, is the average daily rate of Mercury for a 
period of nearly 100 years. We have, then, 

360 -f- 4.09234 = 87.9692 days, =87 d. 23 h. 15 m. 57 
sec, the exact length of Mercury's year. 

DISTANCES OF THE PLANETS FROM THE SUN. 

269. Unit of measure. — We measure length by com- 
parison. A piece of cloth we compare* a certain number 
of times with a rod whose length we call a yard. The dis- 
tance between two cities we measure with a length which we 
call a mile. Even if the yard-stick were lost, we might 
measure the cloth with any rod which we happen to have, 
and afterward, when we have compared our rod with a yard 
measure, reduce the length of our cloth to yards. The 
measuring-rod with which we obtain the planetary dis- 
tances is the radius of the 

earth's orbit, although we 
have not yet found the 
length of this rod. We 
compare other distances 
with this, and by this 
means we may be able 
indirectly to find the 
length of this quantity, 
which we could not deter- 
mine directly (190). When 
that is found, our results 
may be changed from one 
denomination to the other, 
— from radii of the earth's orbit to miles. 

270. Distance of an inferior planet —Elongation. — 
The elongation of a planet is its angular distance from the 




* Con-parO) to make equal with 



140 ELEMENTS OF ASTRONOMY. 

sun. Let E represent the earth, and V an inferior planet, 
as Venus. (Fig. 89). When EV is tangent to the planet's 
orbit, the angle of elongation, VES, is evidently greatest 
for that revolution of Venus. In the triangle VES, the 
angle E is known, V is a right angle, and SE is the radius 
of the earth's orbit, our unit of measure. The value of 
VS, found by the methods of plane trigonometry, is some 
fractional part of that unit. 

271. Orbits not circular. — At different times the great- 
est elongations vary, as shown in the table. From this it 
appears that the radii of the orbits vary in length; the data 
show that the orbit of Mercury has considerable eccentricity, 
while that of Venus is not circular. A series of calculations, 
using both the varied elongations, and the different radii 
of the earth's orbit, as found at the time of observation, 
would give plans of the orbits very nearly. 





Mercury. 


Venus. 


Least extreme elongation, 


i7° 37' 


44° 58' 


Greatest " " 


28 4 


47 3° 


Mean 


22 46 


46 20 


Mean radius, 


0.387098 


0.723332 



272. Distance of a superior planet. — Let S, E', and 

M' represent respectively the sun, the earth, and a superior 




planet, as Mars, on the day when the planet is in opposition 
(261). Mars appears in the sky in the line E'M'A. On 
the day after opposition, the earth has moved to E, and 



KEPLER'S THIRD LAW. 



141 



Mars to M; the angles ESA and MSA are easily found from 
the known rates of the planets. Because of the great dis- 
tance of the sky, a fixed star, which, on the first day, was 
seen in the line E' A, now appears in the same direction on 
the parallel line EB, while Mars seems to have moved back- 
ward from the star by the amount of the angle AEB. This 
angle is easily observed: as EB and SA are parallel, it is 
equal to EAS. 

In the triangle ESM, we have ES, the radius of the earth's 
orbit ; 

SEM = 180 — (ESA + AEB), (Geom. 255); 

ESM= ESA — MSA ; 

EMS = EAS + MSA, (Geom. 261); 

A trigonometrical solution gives the side MS, which is 
desired. 

273. Table of Planetary Revolutions. — 



Name. 


Relative Distance. 


Synod. Rev. 


Sid. Rev. Days. 


Sid. Rev. 


Mercury, 


°-3 8 7°99 


H5-9 


87.97 


3 mos. 


Venus, 


0.723332 


583-9 


224.70 


-1/ » 


Earth, 


1. 




365.26 


1 year. 


Mars, 


1. 523691 


779.8 


686.98 


23 mos. 


Jupiter, 


5.202800 


398.8 


4332.58 


12 vrs. 


Saturn, 


9.538852 


378.0 


IO759.22 


2 9 y 2 « 


Uranus, 


19.18338 


369-7 


30686.82 


84 " 


Neptune, 


3°-°5437 


367-5 


60126.71 


165 » 



KEPLER'S THIRD LAW 



274. After comparing in various ways the tunes of the 
planets and their distances, Kepler discovered his third law 
of planetary motion : 

TJic squares of the times <//>• in proportion to the cubes of 
the moan distances from the sun. 



142 ELEMENTS OF ASTRONOMY. 

This most remarkable law, applying as it does to all the 
planets in their circuits about the sun; to the satellites, as 
they revolve about their primaries; even to the members 
of the far-off stellar systems in the remote regions of the 
universe, proves that all these objects have a similar origin 
and are subject to the same government. Nature works with 
uniformity in all her vast domain. 

This law is practically useful in determining the mean 
distance of a newly-discovered planet. The rate of motion 
of the stranger would be first observed; from this its time 
of revolution is computed, and its distance obtained. Thus, 
if a planet were found whose period is 5 years, 

i 2 : 5 2 :: I 3 : x z . \ x = $ / 2$ = 2.924 -j-. 

The distance of the planet from the sun would be 2.924 
times the mean radius of the earth's orbit. 

Distances obtained by Kepler's ' third law are deemed 
more reliable than those derived from other sources. 

275. Actual distances not yet found. — As yet we 

have found only the relative distances of the planets, when 
compared with the distance of the earth from the sun, taken 
as a unit of measure. One of these distances positively 
known, would help as to all the rest. When Mars is nearest 
the earth, his distance from the sun is about one and one 
half, and, therefore, his distance from the earth is about one 
half, the distance from the earth to the sun. When so near, 
his parallax may be found. 

276. Observations of Mars. — From 1700 to 1761, 
astronomers observed Mars with the greatest care, and ob- 
tained the best results which could be given by instruments 
which were reliable only to two seconds of arc. In 17 19, 
Maraldi found the parallax of Mars to be 27". The distance 
of the planet from the sun was at that time 1.37; from the 
earth, .37. But parallax is the angle which the radius of the 
earth subtends to an observer at the distant object (178): it 



TRANSITS OF VENUS. 



143 



is, therefore, inversely in proportion to the distance of the 
object. Hence, 

Sun's dis. : Mars' dis. : : Mars' par. : Sun's par. ; 
1 : 0.37 : : 27" : 9. 99", nearly 10". 

TRANSITS OF VENUS. 



277. In 1725, Dr. Halley explained a method of finding 
solar parallax by observations of the transits of Venus, taken 
from remote points on the earth. The 

next transits of Venus occurred in 1761 
and 1769. The problem to be solved 
was deemed so important that the gov- 
ernments of France, England, and Russia 
sent expeditions to various parts of the 
earth to secure observations. It was 
while engaged in this business that the 
celebrated navigator, Cook, lost his life 
at Hawaii. Le Gentil went to India to 
observe the transit of 1761, but, because 
of detentions on the voyage, he arrived 
too late. He waited the eight years for 
the next transit, and was then disap- 
pointed by the passage of a cloud over 
the sun at the critical time. 

Delisle devised another method, some- 
what more readily explained, from con- 
sidering the transits of 1761 and 1769. 

278. Delisle's method. — Suppose 
that two persons, each provided with a 

suitable telescope and an astronomical 
clock, arc at distant places on the earth, 
A and />, looking for an expected transit. 
When Venus comes to the position /'. 
the observer at .7 sees her apparently touch the sun: he notes 




Fi 



g. 91. 



144 



ELEMENTS OF ASTRONOMY. 



the time of contact. A little later, the observer at B marks 
the time at which Venus seems to touch the sun in the posi- 
tion V . Between the two observations, the earth has moved 
over the arc EE' , which measures the angle ASA, and Venus 
has moved over the arc VV , opposite a somewhat larger 
angle ASB. The value of each angle is found from the 

known rates at which the 
planets move. The differ- 
ence between these two an- 
gles, the small angle ASB, 
or the amount of angular 
motion which Venus gained 
in order to make the contact 
visible at B, is the parallactic 
angle sought, opposite the 
base-line AB. 

The observation is repeated 
by noting the time of external 
and internal contact on each side of the sun's disc. 

279. Halley's method. — To an observer at A, Venus 
seems to cross the sun's disc on the line ef ; to one at B, 




Fig. 92. 




Fig- 93. 

on the line ab. The two lines AD and BC, from the 
images on the sun to the observers, cross at V, making the 



TRANSITS OF VENUS. 



45 



angles at V equal : the three bodies, E, V, and the sun, are 
in the same plane, and the lines AB and CD, perpendicular 
to that plane, are parallel. Hence, the triangles A VB and 
CVD are equiangular; but equiangular triangles have their 
like sides proportional; hence, 

AB : CD : : A V : VD. 
AD = i; VD=.J2^ (273); therefore, AV=i — .723=. 277. 
Hence, AB : CD :: .277 : .723. 

Put for AB the distance in miles between the two places 
of observation; reduce, and we have the value of CD, the 
distance between the two chords ab and ef, on the sun's 
surface, in miles. 

During this observation, the sun has an apparent eastward 
motion, at a certain rate ; Venus has a westward motion, at 
a different rate; the sum of the two rates gives the apparent 
rate of the planet over the disc of 
the sun — so many seconds of arc in 
one second of time. Having noted 
carefully the time occupied in cross- 
ing the sun's disc, the length of the 
line of passage is known in seconds 
of arc. Construct the right-angled 
triangle COb, in which Cb, half the 
line ab, and Ob, the radius of the 
sun's disc, are known in seconds; 

by construction, or, better, by trigonometry, the triangle is 
solved, and CO is found. In the same way, from the tri- 
angle DO/, DO is found. DO taken from CO leaves CD, 
the distance between the chords, in seconds. 

We know now how many seconds a certain number of 
miles will subtend at the distance of the sun. 

Th? sun's parallax is the angle which the radius o( the 
earth subtends at the distance of the sun (191) j hence, 

CD in miles : CP in seconds :: 




Fig. 94- 



Earth's Rad. in miles 

Ast. — xo. 



Sun's hor. 



par. 



146 



ELEMENTS OF ASTRONOMY. 



280. Other methods of investigation. — The impor- 
tance of the solar parallax and of the sun's distance from the 
earth as a unit of astronomical measurement, has caused the 
problem to be attacked from many directions. Professor C. 
A. Young enumerates thirteen methods, most of which are 
too abstruse to be discussed here. Among them may be 
mentioned calculations based upon observations of Mars 
when near opposition (276); of some of the nearer asteroids 
in similar positions; of Venus when at or near inferior con- 
junction, as above explained; of certain inequalities in the 
moon's motion; of the perturbations of the planets; of the 
velocity of light. 

The transits of Venus in 1761 and 1769 were discussed by 
Encke, and the value of the parallax was placed at 8.5776". 
From this the distance of the earth from the sun was com- 
puted at about 95 millions of miles (95,274,000), which was 
long used as the accepted value. Astronomers have found 
great difficulty in agreeing upon the solar parallax. Among 
the results obtained are the following: 



281, 



CALCULATIONS BASED UPON 




AUTHORITY. VALUE 


IN 


SECONDS. 


Transits of Venus, 1761-69, 






Encke, 


8.5776 


do do 






Powalky ; Stone ; Fay ; 


8 


7 to 8.9 


do 1874 






Airy, 


8 


76 


do do 






Tupman, 


8 


81 


do do 






Stone, 


8 


88 


Opposition of Mars, 1862, 






Newcomb, 


8 


855 


do do 






Gill, 


8 


783 


Observations of the Moon, 






Hansen and others, 


8 


83 to 8.92 


Perturbations of Planets, 






Leverrier, 


8 


86 


Velocity of Light, 






Cornu ; Michelson 


8 


78 to 8.85 


do 






Todd, 


8 


808 


Investigations of all known 


data, 


1865, 


Newcomb, 


8 


848 


The British " Nautical Almanac ' 


' uses, 




8 


95 


The Berlin " Yahrbuch " and American 


"Ephemeris" uses, 


8 


848 


The French " Connaissance 


de T 


emps " 


uses, 


8 


86 



Prof. C. A. Young gives, as the result of careful investiga- 
tion, the value 8.8 as that having the greatest probability. 



DIAME TERS OF HE A VENL Y B ODIES. 1 4 7 

The corresponding value of the mean radius of the earth's 
orbit is 92,885,000, with a possible error of 225,000 miles. 
It is, therefore, sufficiently exact for the ordinary student to 
call the distance of the earth from the sun 93 millions of 
miles. 

A difference of one hundredth of a second in parallax 
produces a difference of about 112,000 miles in distance. 

DIAMETERS OF HEAVENLY BODIES. 

282. The Sun. — We now have more exact quantities, 
which may be substituted for the approximations previously 
used (191), to determine more nearly the sun's true diameter. 
Insert the sun's parallax, and the sun's apparent radius, 
1 6' 2", observed at the same time, and we have 

8.8" : 962" : 7913 : 863,898, 

the sun's diameter. More exactly 866,400. 

283. Diameter of Venus. — We find the horizontal par- 
allax and corresponding radius for the same day. For 
example, Jan. 1, 1883, they were, parallax 25.3", radius, 
24.4"; then, 

253 : 244 : : 7913 : 7632, Venus's diameter. 

284. Diameter of Jupiter. — The parallax of Jupiter 
can not be measured on account of his distance. 

The radius of the earth will seem to diminish as the dis- 
tance at which it is seen increases. If Jupiter is four times 
as far from the earth as the sun, the radius of the earth will 
seem to an observer at Jupiter one fourth as large as to an 
observer at the sun. Jupiter's mean distance is 5.2028 (273); 
hence, 

5.2028 : 1 :: 8.8" : 1.60" -| - Jupiter's parallax. 

Then, as before, 

1.69" : 18.26" :: 7913 : 85400 — = Jupiter's diameter. 



148 ELEMENTS OE ASTRONOMY. 

285. Size of the planets. — Spheres are to each other 
in volume as the cubes of their like dimensions; that is, 

(Dia. ofE.) 3 : (Dia. of Sun) 3 :: Vol. of E. : Vol. of S. 
7913 3 : 866, ooo 3 : : 1 : 1,300,000, nearly. 

The average diameter of Jupiter is 10.8 times that of the 
earth; hence, 

i 3 : 10.8 3 :: 1 : 1260, nearly: 

the volume of Jupiter is 1260 times the volume of the earth. 
Similarly, the diameters and volumes of other planets may 
be found. 

MASSES OF THE HEAVENLY BODIES. 

286. Definition. — The mass of a body is the quantity 
of matter which it contains. The weight of a body on the 
earth measures the force with which the earth attracts that 
body, and the attraction is in proportion to the quantity of 
matter, or its mass. Hence, the mass of a body is indicated 
by its weight. 

The mass of a cubic foot of iron is greater than the mass 
of a cubic foot of ice, because the particles are more densely 
packed in the iron than in the ice. Hence, the mass is 
in proportion to the density, and the weight indicates the 
density. 

287. Motion of a falling body. — Experiments prove 
that a body falling near the surface of the earth passes 
through 16.08 feet in the first second; four times that space 
in 2 seconds ; nine times that space in 3 seconds, and so on : 
the distance for any number of seconds is 16.08 feet multi- 
plied by the square of the number of seconds. 

288. Downward motion of a projectile. — A projec- 
tile is any thing thrown into the air — a cupful of water, a 
stone, or a cannon-ball. Aim a cannon horizontally, and 
place it where the ball may strike a vertical wall in one 



MASSES OF THE HEAVENLY BODIES. 



149 



second; the ball will not follow the horizontal line of the gun, 
but will strike the wall 16.08 feet below that line; this has 
been proved by actual trial. The ball is drawn toward the 




B+- 



earth precisely as far as one which falls vertically from the 
mouth of the gun in the same time. 

If the wall is so far away that the ball requires two seconds 
to reach it, the ball will strike 4 X 16.08 feet below the 
horizontal line. 

289. The measure of gravity. — We consider 16.08 
feet a measure of the attractive force of the earth, at its sur- 
face. If the mass of the earth were 

greater, and consequently its attractive 
power greater, it would draw the falling 
body with more force, and, consequently, 
make it move with greater speed. 

290. The moon a projectile. — In 

the moon's revolution about the earth, it 

has a forward motion, which, with the 

earth's attraction, determines its path 

(204). Let A be the place of the earth. 

By that of the moon, and suppose the 

moon to be driven on the line />'(' by 

a force which will move it to (' in one 

second of time. Because o{ the earth's attraction, the moon 

will not go to O but will tome to the line AD at A as if it 




150 ELEMENTS OF ASTRONOMY. 

had fallen through the distance CD. CD is, therefore, the 
measure of the earth's attraction at the distance of the moon. 

291. The moon obeys the law of gravitation. — 

Gravity varies inversely as the square of the distance (157). 
Hence, 

The moon's distance 2 : The earth's radius 2 : : 

Gravity at earth's surface : Gravity at the moon, 

or 240, ooo 2 : 4000 2 :: 16.08 ft. : 0.004464 ft. ; 

the distance through which the moon should fall per second 

in obedience to the earth's attraction. 

In the triangle ABC, the side AB is known, being the 
distance of the moon; the angle B is a right angle; and the 
angle A, the angle of the moon's motion in one second : from 
these, we calculate the side AC. From AC take AD, and 
there remains CD, the distance through which the moon 
falls; it is 0.0044621 feet, and corresponds very closely to 
the preceding amount. 

Closer calculation removes even this difference, and thus 
it appears that the space through which the moon actually 
falls per second is the same as that which the force of 
gravity would cause it to describe. 

292. The earth falls toward the sun as the moon 
falls toward the earth. In the same figure, let A be the 
place of the sun; B, that of the earth; CD, the amount of 
space through which the earth falls; that is, through which 
the sun draws the earth in one second. As before, 

93,ooo,ooo 2 : 4000 2 : : 16.08 : x, 

the distance through which a body would fall in one second, 
at the distance of the sun, if attracted with a force equal to 
that of the earth. But, working the other part of the prob- 
lem, as in the case of the moon, we find the actual space 
about 330,000 times the result found in the proportion. 
Hence the sun's attractive power is about 330,000 times as 
great as the earth's attraction would be in the same place, 



RECAPITULATION. 151 

and, therefore, the sun's mass must be about 330,000 times 
the earth's mass. Professor Young gives 330,000 zh 3000. 

293. The mass of Jupiter is found from the motion 
of his satellites in the same way. First find how ^far one 
of Jupiter's satellites should fall if the sun were at its 
center of motion; then find how far it does fall. The 
ratio of the two quantities is the ratio of the sun's mass to 
Jupiter's mass. The method applies to any planet which 
has a satellite. 

294. The mass of Venus. — The mass of a planet 
which has no satellite is computed from its effect in dis- 
turbing other bodies, as it comes into their vicinity. The 
method is too abstruse to be introduced into a work of 
this character. 

295. Densities. — The density of a body is the quantity 
of matter contained in a unit of space, as a cubic inch, 
yard, or mile. It is found by dividing the whole mass by 
the whole volume. To compare the density of a planet, 
as Jupiter, with that of the earth: find what mass Jupiter 
would have, if of the same density as the earth, by the 
proportion, 

Vol. of E : Vol. of J : : Mass of E : Mass of J. 

If this supposed mass is equal to the actual mass (293), 
the densities of the two bodies are equal. 

296. RECAPITULATION. 

Measurements on this small globe bf ours, enable us to determine: 

1. The relative distances of the sun and planets. 

2. The shapes of their orbits. 

3. The times in which they revolve about the sun. 

4. Their actual distances. 

5. Their dimensions. 

6. Their masses. 

7. Their densities. 



CHAPTER XII. 

THE SUN. 

297. The sun's power. — We recognize in the sun the 
center of light, heat, and attraction for all the members of 
the solar system. We find in him the spring of all vital 
action, either vegetable or animal, on our earth; the origin 
of most mechanical power, producing winds, tides, currents, 
lifting all the water which falls in rain or thunders in cataracts, 
and exciting electric and magnetic forces. Immense as this 
work done for us by the sun is, its entire action on the earth 
is but the 2300 millionth of the entire force generated by 
the sun ; that part is all that our earth can intercept of the 
influence which radiates from the sun in all directions. 

Many believe that the sun is the common origin of all the 
planets and satellites ; that his volume once filled the immense 
space now surrounded by the orbit of the remotest planet ; 
and that, as this volume contracted in size, one after another 
of the planets was thrown off as a nebulous ring, which after- 
ward consolidated into a planet, and, perhaps, imitated this 
action in the evolution of satellites. 

298. Ideas of the sun's greatness. — In the last chap- 
ter, we found the distance from the earth to the sun to be 93 
millions of miles (281); his diameter, 866,400 miles (282); 
his mass, 330,000 times that of the earth (292); and his 

density, one fourth the earth's density. 

(152) 



THE SUN. 



153 



LIMBo/> { 



From these abstract numbers, we obtain very indistinct 
ideas of absolute dimensions. We learn to estimate distance 
by the time required to traverse that distance : thus, we say 
that New York is so many hours by rail from Chicago, rather 
than so many miles. So we may get a notion of the sun's 
distance, if we estimate that an express train, running without 
interruption 30 miles an hour, 
would require more than 350 
years to reach the sun, and that 
a telegraphic signal could not 
be answered in less than two 
hours and a half. 

Were the center of the sun 
placed at the center of the earth, 
its surface would extend to nearly 
twice the distance of the moon's 
orbit. 

The volume of the sun is 
1,300,000 times that of the 

earth. A French instructor, wishing to illustrate the relative 
volumes of the earth and sun, laid down a single grain of 
wheat to represent the earth. He then estimated the quantity 
which 1,300,000 grains of wheat would make, and poured 
the* wheat in a pile, to represent the bulk of the sun; it re- 
quired about 4 bushels. 

The mass of the sun might be expressed in tons, but 
the long array of figures would give no definite or valuable 
idea. It is about 330,000 times that of the earth, and 
about 750 times that of all the known bodies which revolve 
about him. 




Fig. 97. 



299. The sun from other planets. — The intensity oi 
solar light, heat, and attraction varies inversely as the square 
of the distance (157). The apparent breadth oi the sun 
varies inversely as the distance (182). The figure shows the 
relative size oi the sun as viewed from the various planets. 



154 



ELEMENTS OF ASTRONOMY. 
F SUN AS Jff/V FROM 



O 
URANUS 




THE PHYSICAL NATURE OF THE SUN. 

300. Solar spots. — When viewed through a piece of 
smoked or colored glass, to protect the eye from the intense 
light and heat, the sun shows a round disc, of a uniform 
golden hue; in a telescope of moderate power, its surface is 
often seen to be marked by irregularly placed dark spots. 
Observations of the same spots, continued from day to day, 
show that they appear at the eastern limb, cross the disc in 
about fourteen days, and vanish at the western edge; they 



THE PHYSICAL NATURE OF THE SUN 155 

often re-appear in about four weeks from the time when first 
seen. At first the spot shows merely a dark line, parallel 
with the edge of the sun; as it advances, it grows broader, 
and after it has passed half way across the disc, it diminishes 
again to a line. The motion seems more rapid near the 
center of the disc than near the margin. From the varied 



Fig. 99. 

figure and rate of motion of the spots, it appears that the 
sun is spherical, while the fact of their movement indicates 
a rotation of the sun on its axis. A dark spot painted on 
a globe presents similar appearances, if the globe is made 
to rotate. 

301. Time of the sun's rotation. — The spots seem 
to complete a revolution in 27.5 days, but some of this time 
must be due to the motion of the earth ; the spot and the 
earth perform a synodic revolution (265) in that time. If the 
sun were to rotate only as fast as the earth revolves about it. 
the spots would appear stationary; hence, the motion of the 
earth apparently cancels one rotation of the sun in each year. 
The sun seems to make 365.25 -5-27.5= J 3- 2 ^ rotations in 
a year, and really makes 14.28 rotations in that time, or one 
in 25.38 days. 

302. Position of the solar axis. — In June and De- 
cember, the spots appear to cross the disc in straight lines; 
in spring, the lines curve toward the northern margin; in 
autumn, toward the southern margin. From this, it appears 



156 



ELEMENTS OF ASTRONOMY. 



that the axis of the sun is inclined to the plane of the earth's 
orbit, and that the spots describe parallels of solar latitude 




Fig. ioo. 

which seem to curve from the pole which is nearest the earth. 
The inclination of the axis is 7 ° 15'. 

The spots appear only in a belt, called the royal zone, 
extending about 35 ° on either side of the solar equator. 

Besides the general movement from the eastern to the 
western margin of the sun, as seen from the earth, the spots 




Fig. 101. — Solar Cyclone. 

have irregular motions of their own, so that a spot may seem 
to be hurried, or delayed, to diverge to right or left; some- 
times they show a whirling motion. 



THE PHYSICAL NATURE OF THE SUN. 



57 



303. The appearance of a spot. — It consists usually 
of a dark part, called an umbra, surrounded by a gray, 
furrowed border, called a penumbra. The edges of both 
portions are ragged and irregular; several umbrce are often 
inclosed in a single penumbra, the gray portion seeming to 
make bridges across the dark. Often there are penumbrae 




Fig. 102. 



with no dark center, and umbrsa with no gray margin. The 
penumbra is darkest near its outer edge, and brightest near 
the dark portion. In the umbra, a still darker part, called the 
nucleus, has lately been observed. It is possible that none 
of the shades are really black, but only seem so by contrast 
with the brilliant dise o\ the sun, since the most intense arti- 
ficial light shows black against the sun's disc. Transits of 
Mercury prove that the umbra is not so dark as the unillu- 
minated side of a planet. 



158 ELEMENTS OF ASTRONOMY. 

304. Dimensions and variability. — Many have been 
visible without a telescope. Diameters are recorded of 
29,000, 50,000, and 74,000 miles; in 1839, a spot ap- 
peared, whose penumbra was 186,000 miles long. The 
largest recorded spot was seen in 1858; it covered one thirty- 
sixth of the sun's surface, and had a breadth of 143,000 




Fig. 103. — Changes in sun-spots during one rotation of the sun, observed 
the 24th May and 21st June, 1828. (Pastorff.) 



miles. Were these spots cavities in the substance of the sun, 
our earth would lie in one of them like a bowlder in the 
crater of a volcano. In form and size, the spots vary rapidly 
and constantly. It is often difficult to recognize them as 
they re-appear, and even under the eye of the observer they 
change materially. When a new spot appears, the umbra 
is first seen, then the penumbra, afterward the nucleus 
within the umbra; the whole often attains its full size in a 
single day, and may vanish as soon, or remain for weeks, or 
even months. When the spot vanishes, the sides contract 
to a point, the penumbra closing last. While the spot is 
increasing, the edges are sharp and well denned; as it van- 
ishes, they seem to be covered with a mist or vail. 



THE PHYSICAL NATURE OF THE SUN 



r 59 




Fig. 104. — Details of groups A and B, in last figure. 



305. Periodicity. — The number and size of the spots 
vary greatly in different years. Wolf has examined the 
records from 16 10, and has found the successive periods 
of greatest and least abundance. The times between suc- 
cessive periods of greatest numbers vary from seven to six- 
teen years, but have an average of about 11^ years. The 
last maximum was probably in 1882. An attempt has been 
made to connect this recurrence of sun-spot years with the 
conjunctions or oppositions of some of the planets, partic- 
ularly Mercury, Venus, and Jupiter, but the periods do not 
correspond with sufficient closeness, and it would be difficult 
to understand how the planets could cause such results. 

Certain magnetic disturbances on the earth are found to 
occur most frequently when the sun-spots are most abund- 
ant. The aurora borcalis is most frequently scon at the same 
periods. Cyclones at sea and tornadoes on land have been 
observed to be numerous and destructive in sun-spot years. 
notably in 1882. If these phenomena have a mutual de- 
pendence, as seems likely, it has not yet been discovered. 

306. Faculae. — Curved and branching streaks more bril- 
liant than the rest oi the sun, quite distinct in outline and 
separating into ridges and net work, are often seen near large 



160 ELEMENTS OF ASTRONOMY. 

spots, or where spots have vanished, or where they after- 
ward appear. They are called faculce, little torches. They 
are of all magnitudes, from barely discernible narrow tracts 
iooo miles long, to complicated and heaped-up ridges 
40,000 miles long by 1000 to 4000 miles wide. 

Mr. Dawes has proved that these are mountainous billows 
of luminous matter raised above the general surface. In 




Fig. 105.— Mottled surface of sun.— Secchi. 

1859, he observed a ridge near the edge of the sun, project- 
ing like a range of hills, whose height could not be less 
than 500 miles. 

307. The general surface of the sun has a mottled 
appearance, easily observed, even with small telescopes. 
(Fig. 105). In a large instrument, the surface seems com- 
posed of patches of light, separated by rows of minute, dark 
spots, called pores. The luminous masses have been com- 
pared in shape to "willow-leaves," "rice-grains," "granules," 
"things twice or thrice as long as broad," etc. They may 
be distinct masses of luminous matter, or simply waves, 



THE POLARISCOPE. 161 

ridges in the grand ocean of flame, continually changing in 
outline and position, like waves in the sea. They are not 
seen on the faculae, but similar forms surround the margins 
of penumbras, stretching out toward the interior of the spot. 

308. Depression of the spots. — That the spots are 
hollows in the general surface of the sun is shown by the 
appearance of the penumbra as it moves over the sun's disc. 
Dr. Wilson observed, in 1769, that while the spot is near the 
eastern margin, the penumbra is wanting on the side nearest 
the center of the sun's disc ; as the spot moves on, the 
penumbra shows about equal breadth on either side; and as 
the spot approaches the opposite limb, the breadth of the 
penumbra is greatest on the farther side. These variations 
are clearly shown in Fig. 98. 



THE POLARISCOPE. 

309. When the light passes through certain substances, as 
a thin slice of tourmaline, or of Iceland spar, properly ar- 
ranged, a peculiar effect is produced, called polarization. A 
description and explanation of these effects, and of the vari- 
ous substances which produce them, belong to the science 
of optics. It is enough for our purpose to know that these 
effects, though various, are uniform in light which comes 
from the same kind of source. The instrument used is called 
a polariscope. By it the observer can distinguish between 
emitted and reflected light, and between the light furnished 
by a glowing solid, as platinum ; a liquid, as melted iron or 
glass; or a gas, as the (lame produced by the burning of a 
candle, of illuminating gas, etc. 

Arago determined that the light of the sun is such as is 
emitted from a burning gas, a llame. This analysis indicates 
that the visible surface of the sun, called the photosphere, is 
composed o( gaseous matter in intense combustion. That it 
is nut a solid is shown by the very rapid changes seen in the 

Ast.— 11. 



1 62 ELEMENTS OF ASTRONOMY. 

spots and facube. The faculae and willow-leaved "things" 
are but the billows in this grand ocean of flame; they are 
masses which appear brighter on account of the greater 
intensity of the flame, or on account of the position in which 
they lie in respect to us, since the edge of a flame is brighter 
than its side. Henry and Secchi have each shown that the 
dark spots emit less heat than the luminous surface. 



SPECTRUM ANALYSIS. 

310. The solar spectrum. — A ray of sunlight admitted 
into a dark room shows a round, white spot upon a screen 
which receives it. If a prism be placed in its path, the 
white spot is refracted to a different place on the screen, and 
is extended into a long band, called the solar spectrum, which 
shows all the colors of the rainbow. In 1802, Wollaston 
discovered dark lines, which cross the spectrum in various 
places. They were afterward called Fraunhofer's lines, from 
a German optician who named those most easily observed, 
and carefully mapped their places. From 600 to 2000 are 
seen with spectroscopes of various powers. 

311. Spectrum analysis. — When we analyze light from 
a flame which contains some metallic vapor in combustion, 
certain colored lines are produced, which are peculiar to 
the substance burned. Thus, sodium shows its presence by 
two very fine, bright yellow lines placed close together, all 
the rest of the field being perfectly dark. The sign of 
potassium is a bright red line near one end of the spectrum 
and a bright violet line near the other end. In 181 5, Fraun- 
hofer observed that the yellow lines coincide in position 
with two dark lines in the solar spectrum; in 1842, Brewster 
noticed a similar fact in regard to the potassium lines. 

312. Laws of spectrum analysis. — KirchhofT found 
that when the rays of a flame colored with sodium, for 



PHENOMENA OF SOLAR ECLIPSES. 163 

example, pass through vapor of sodium, the bright lines in 
the spectrum vanish, and black lines appear in their places. 

By these and similar experiments these laws of spectrum 
analysis have been determined. 

1. When solid or liquid bodies emit light, their spectra are 
continuous, unbroken either by dark or bright lines. 

2. Every element or compound that emits light when in 
a gaseous condition, is distinguished in the spectrum by bright 
colored lines peculiar to itself. 

3. Vapors of metals or gases neutralize or absorb the 
colored rays which they would themselves emit. 

313. The nature of sunlight. — Let a prism be so ar- 
ranged that a beam of sunlight is decomposed by one por- 
tion, while a beam from burning gas, containing vapor of 
some substance, as iron, zinc, or sodium, is decomposed by 
another portion, the two spectra being placed side by side. 
The bright lines of the metals are found to coincide pre- 
cisely with dark lines in the solar spectrum, and, by proper 
arrangements of apparatus, the dark lines may be transformed 
into bright lines at the will of the experimenter. Hence, we 
conclude that the dark lines in the solar spectrum which cor- 
respond to iron, for example, are caused by iron burning in 
the sun, the light from which passes through other vapor of 
iron in the sun's photosphere, and has there had its peculiar 
spectral powers absorbed. 

This analysis gives evidence of the presence in the sun 
of twenty-two elements, among which may be named oxygen, 
hydrogen, calcium, sodium, magnesium, chromium, barium. 
nickel, cobalt, iron, copper, manganese, and lead. 



PHENOMENA OF SOLAR ECLIPSES. 

314. Much of our knowledge of the envelope or atmos- 
phere of the sun which lies above the photosphere (309) has 

been obtained when the direct light oi the sun has been 



164 



ELEMENTS OF ASTRONOMY. 



obscured in a total eclipse. (Fig. 106). The most notable 
phenomena then observed are the corona, with its luminous 
streamers, and the red prominences. 




Fig. 106.— Eclipse of August, iS 



315. The corona. — When an eclipse of the sun becomes 
total, as the last gleam of direct sunshine vanishes, a beau- 
tiful vision appears in the darkened sky. The black disc 
of the moon is surrounded by an effulgence of radiant, 
pearly light, that is feebly represented by the halo which 
painters draw about the heads of saints. Near the moon, 
the tint is rosy; thence emanate an infinity of rays of white 
and yellow and violet light. This glory is called the corona. 



PHENOMENA OF SOLAR ECLIPSES. 



165 



Its duration at any eclipse is rarely so long as five minutes, 
and these minutes astronomers deem very precious. 

The ring of light about the sun has a breadth rather uni- 
formly three or four minutes of arc. (Fig. 107). Beyond 
this ring irregular rays or streamers reach a much greater 
distance, sometimes traceable as far as six or seven degrees 
of arc. 

It will be remembered that a minute of arc means at the 
sun a distance of nearly 28000 miles; a degree of arc means 




Fig. 107. — Eclipse of July, 1860. 



more than 1600000 miles, or nearly twice the sun's diameter. 
A series of drawings of solar eclipses shows remarkable vari- 
ations in the position, form, and extent of these luminous 
radiations. 

316. Where is the corona? — It has been by some 
accounted for as merely an effect of the sunlight in the 
atmosphere of the earth, or o\ the moon. Bui the radiance 
centers not in the moon, hut in the sun, and the moon passes 
by the corona, instead o( carrying it forward with itself. 
Young believes that observations made bv himself, ami 



1 66 ELEMENTS OF ASTRONOMY. 

independently by Harkness, in 1869, settle conclusively that 
the corona is a manifestation of the sun's atmosphere. Each 
saw in the spectroscope (310) a bright green line — the famous 
1474 line, so called from its place in the Kirchhoff scale — 
which proves the presence of a burning gas in the corona, 
and, therefore demonstrates its connection with the sun. 




Fig. 108. — The sun, with protuberances and red flames, July 23, 1871. After 
Secchi. The figures mark the flames, 17 in number. 



317. What is the corona? — The lower part is the 
sun's atmosphere, made luminous by heat and by reflection. 
The cause of the streaming rays has not yet been found. 

318. The red prominences are also seen at the time of 
totality in a solar eclipse. (Fig. 108). They are flame-like 
emanations in the lower regions of the corona, as varied in 



PHENOMENA OF SOLAR ECLIPSES. 167 

form, and often as fantastic, as the clouds in our summer 
skies. The larger ones may be seen without any magnifying 
power extending 3' from the sun. 

Previous to the solar eclipse of 1868, special preparations 
had been made for studying the lines of the red prominences 
with the spectroscope, while the sun was obscured, and the 
results were successful. Then the discovery was made, by 
Janssen and by Lockyer, independently, that these phenomena 
could be seen by directing the instrument to the edge of the 
sun's disc at any time, and without waiting for an eclipse. 
Since then, Huggins, Zollner, Respighi, Young, and others 
have made careful studies of these most interesting forms. 

319. What are they ? — Young describes them as qui- 
escent, or hydrogenious, and eruptive, or metallic. The qui- 
escent forms, in their resemblances and differences, are like 
the clouds in our own atmosphere. Great masses lie without 
change for hours, and even during a whole solar rotation. 
They are often connected to the sun's surface by falling 
fringes, which suggest summer showers. Secchi has seen 
these cloudlets form and grow as clouds form at the earth. 
Their spectra indicate the presence of hydrogen with sodium 
and magnesium. 

The eruptive prominences are brilliant jets thrown up from 
the sun's surface, often with tremendous energy. Their 
spectra show the presence of numerous metals in great abund- 
ance. These prominences are frequent near sun-spots, and 
are particularly abundant near faculse. 

320. Their magnitudes. — Their altitudes are usually 
not more than 20,000 miles. A few reach up to 80.000 or 
100,000 miles high. Serchi saw one of 300,000 miles, and 
Young, in 1880, saw one reach the enormous elevation oi 
350,000 miles. The movement o\ this eruptive discharge 
may illustrate the intense energies which are acting at the 
sun. When first seen, at 10.30 \. m., this prominence was 
about 40,000 miles high, and attracted no special attention ; 



1 68 ELEMENTS OF ASTRONOMY. 

in thirty minutes it had doubled its height; in another hour 
it had reached the great altitude stated; by 12.30, two hours 
from the time when it was first observed, "it had utterly faded 
away. While rising, a rapid rotary motion was seen in its 
lower 'portions. 

SOLAR LIGHT AND HEAT. 

321. The intensity in heating, lighting, and chemical 
power of the sunlight which comes from the margin of the 
disc, is found to be less than that from the central portions. 
If the energy at the center were called 100, that at the 
margin- is as follows: 

Heat rays (Langley), 50, or y 2 . 

Light rays (Pickering), 37, or s/s. 

Chemical rays (Vogel), 13, or Y%. 

This variation will be fully explained if we suppose that 
the sun is surrounded by an atmosphere. The rays which 
come to us from the center of the disc have a relatively 
short path through the solar atmosphere; those from the 
margin a longer path, and a larger part of the energy is 
absorbed. Under such conditions chemical rays are known 
to be most readily absorbed, and heat rays least readily. 

Experimenters differ widely in their estimates of the in- 
tensity of sunlight at' the sun's surface. Foucault and Fizeau 
found it 146 times brighter than the lime-light. Langley 
found it 5300 times brighter than the molten steel in a Besse- 
mer converter. The intensest light from the electric arc has 
been estimated at one fourth and even at one half that of 
sunlight. Yet either the lime-light or the electric arc shows 
as a black spot when viewed against the sun's disc. 

The total quantity of sunlight, stated in candle power, of 
sperm candles, weighing six to the pound, and consuming 
120 grains per hour, is 63 X io 25 (Young). 



THEORIES CONCERNING THE SUN. 169 

322. Solar heat. — John Herschel found that the heat 
received at the earth, the sun being in the zenith, would melt 
ice one inch thick in two hours and thirteen minutes. Re- 
membering that the intensity of heat varies inversely as the 
square of the distance, and also the limited portion which 
the earth can receive, he obtained a result which he expressed 
by saying that if the total heat emitted by the sun could be 
concentrated upon the end of a pillar of ice 45 miles square, 
the ice would be melted, even if flowing into the sun with 
the velocity of light. As Young puts the illustration, if a 
column of ice two and one fourth miles in diameter could 
span the 93 millions of miles between the earth and the sun, 
the sun's heat would melt the whole in one second, and 
change all to vapor in seven seconds more. 

The difficulty of estimating the rate of radiation at high 
temperatures has led to great differences of opinion concern: 
ing the temperature at the sun, as follows: 



Secchi, 1 8, 000, ooo° ; 


later, 


250,000° F 


Ericsson, 4,000,000° 


to 


5,000,000° F 


Zollner and others, 50,000° 


to 


100,000° F. 


Pouillet and others, 3,000° 


to 


10,000° F 


Rosetti, approved by Young, 




18,000° F 



The in tensest artificial heat is about 4,000° F. 



THEORIES CONCERNING THE SUN. 

323. Of structure. — The facts learned about the sun 
since the discovery and use of the spectroscope have added 
much to our knowledge of solar physics, and have wholly 
changed the theories of the sun's structure. Astronomers 
are now substantially agreed upon these points: 

1. The mass of the sun is composed of matter, much o( 
which is recognized as identical with elements found in the 
earth; other materials arc not yet determined. 



170 ELEMENTS OF ASTRONOMY. 

2. The interior mass of the sun is in a gaseous condition 
at a very high temperature of unknown degree, but too high 
to be luminous. 

3. The central gaseous mass is surrounded by a stratum 
several thousand miles thick, cooled to a consistency suffi- 
ciently great to hold in check for a while the central erup- 
tive forces, but occasionally compelled to yield to them and 
to allow the discharges seen as eruptive prominences; this 
stratum, though cooler than the mass within, is still heated 
intensely, and to the degree that makes it brilliantly luminous. 
It is called, for this reason, the photosphere. 

4. The outer part of the photosphere grades into matter 
of less density, forming a gaseous layer in which float many- 
hued masses of incandescent substances. This stratum is 
called the chromosphere, and has been described asa " sheet 
of scarlet fire." 

5. Above the chromosphere, and also separated by insen- 
sible gradations, lies an atmosphere of transparent gases of 
constantly decreasing density. This stratum has a great but 
unknown thickness, and is most clearly seen as the corona, 
at times of solar eclipse. 

324. Of the spots and faculse. — The mass of matter 
in the sun constantly loses heat from its outer portions by 
radiation into space, and that the more rapidly because its 
temperature is so high. The cooler matter of the outer por- 
tions falls in currents towards the center, as rain falls on the 
earth, while the heated interior matter rises in counter cur- 
rents. The alternating currents may be everywhere inter- 
mingled, as if the seething mass were full of rising bubbles 
and descending currents, producing the usual ^appearance at 
the surface of pores and billows (307); or the separate move- 
ments may be massed together in terrific storms, sometimes 
whirling over large areas, sun-cyclones, the rotary movement 
of which is often visible from the earth. The tops of the 
ascending columns are the faculae (306). The descending 



THEORIES CONCERNING THE SUN. 171 

currents carry the matter of the photosphere into the hotter 
interior of the sun, and form depressed cavities, in which 
all the visible material melts away in the intenser heat, giv- 
ing a temporary view of the non-luminous interior. The 
sun-spot is a vortex or maelstrom into which the neighboring 
matter pours, the motion being compensated elsewhere by 
counter upward currents. 

325. Of the red prominences. — These are either 
cloud-like masses of hydrogeneous matter, blown out from the 
interior, and upheld above the chromosphere because of their 
vaporous lightness, or of metallic matter, ejected in streams 
through openings in the denser layer of the photosphere, that 
for a time holds the matter below in check, but yields at 
length to accumulating and explosive forces. This matter 
may ascend to great heights, but soon falls back upon the 
surface of the photosphere. 

326. Of the causes of solar heat. — There are three 
principal theories: 

1. That of combustion ; the chemical combinations of matter, 
illustrated on the earth by the union of carbon and oxygen in 
our fires. To this theory objection is made that we know 
of no adequate supply of fuel. Were the sun solid carbon, 
and were oxygen supplied as fast as needed, the whole 
would burn out in 6000 years. Were the fuel something of 
a more enduring nature, still the prodigal consumption would 
exhaust the whole in a time which would be brief when com- 
pared with the periods of natures changes. 

2. The meteoric theory. — That the heat is produced by the 
continued fall of meteoric bodies upon the sun's surface. It 
is now a settled principle o\ physics that heat and motion 
are but different phases of the same force; that one may be 
changed to the other, and that in no way can either be de 
stroyed. The sudden arrest of a moving bod), as of a 
meteor falling to the earth or the sun, develops instantly an 
amount of heat which is the mechanical equivalent o( the 



172 ELEMENTS OF ASTRONOMY. 

motion stopped. Doubtless some heat is so produced, but what 
can be the source of the meteoric stream which, plunging 
into this insatiable abyss, could alone maintain such a lavish 
expenditure of solar energy? If the heavenly spaces are 
furnished with sufficient store of meteoric bodies to keep the 
sun in action, should not the earth receive a quota from the 
same supply, enough to maintain a large degree of heat in 
it also? 

3. The contraction theory. — That the heat is caused by the 
contraction of the sun's material and its gradual change 
from gaseous to liquid and solid conditions. Each of these 
processes must be accompanied by the liberation of vast 
amounts of heat. Helmholtz has estimated that a contrac- 
tion of the sun's radius of 125 feet per year — equal to a 
mile of diameter in 21 years — would account for all the 
present heat-emission. One second of arc equals 450 miles, 
at the distance of the sun from the earth; to reduce the sun's 
apparent diameter one second, which is as little as could be 
detected, would require 450 X 21 years, or nearly 10000 
years. . " 



327. RECAPITULATION. 

The sun is the center of forces for the solar system. 

Spots appear upon its surface. They are cavities of great and very 
variable dimensions ; rotate from west to east ; show several shades of 
color ; are accompanied by brighter spots, called facul<£. 

The polariscope shows that the photosphere consists of gaseous matter 
at a white heat. 

The spectroscope shows the presence of hydrogen, sodium, iron, and 
other terrestrial substances. 

During solar eclipses a solar atmosphere or corona is visible ; the red 
prominences may be seen at the same time, and at other times by 
means of the spectroscope. The prominences are hydrogeneous or 
metallic. 

Theories concerning the sun. 

The sun contains sorne elements found in the earth. 



RECAPITULA TION. 1 73 

The interior is gaseous, intensely heated ; surrounded by 

1. The photosphere, self-luminous, of glowing flame; 

2. The chromosphere, of lighter, colored flame ; 

3. The atmosphere, of transparent gases. 

The spots are openings through the outer strata into the gaseous 
mass below, caused by descending currents. The /acuta: are caused 
by ascending currents. 

The red prominences are matter ejected from the interior. 

The causes of solar heat are one or all of these : 

1. Combustion. 2. Meteoric bodies which fall into the sun. 3. Con- 
traction and condensation of gaseous matter into denser forms. 



CHAPTER XIII. 

THE MOON. — SYMBOL, J). 

328. Positions as related to the earth and sun. — 

We have learned elsewhere (177-184) that the moon is a 
globe about 2,000 miles in diameter, and that it revolves 
about the earth in an elliptical orbit, at an average distance 
of about 240,000 miles. 

When the sun and moon have the same celestial longitude, 
they are in conjunction (261). They rise, come to the merid- 
ian, and set at about the same time. When their longitudes 
differ by 180 , they are in opposition; one rises as the other 
sets. The places of opposition and conjunction, when 
spoken of together, are called the syzygies. When the moon 
is midway in the sky between opposition and conjunction, 
90 from either, it is in quadrature. The four points 
between the syzygies and quadratures are called octants. 

329. Lunar periods. — The time occupied by the moon 
in passing through all the aspects from conjunction to con- 
junction again is called a lunation. It is the same as a synodic 
revolution (265). Its mean length is 29 d. 12^ h. (29 d. 
12 h. 44 m. 3 sec). 

The time of a mean sidereal revolution is 27 d. 7^ h. 
(27 d. 7 h. 43 m. 11. 4 sec). 

330. The synodic revolutions not equally long.— 

When a body moves in an elliptical orbit, its rate of motion 

is so varied that its radius vector describes equal areas in 
( 174) 



THE MOON. 



175 




equal times (201); hence, the body moves fastest when 
nearest the focus. If, then, the space 2-3, which the moon 
has to traverse in order to over- 
take the sun after finishing 
its sidereal revolution, is near 
apogee, where the moon moves 
slowly, more time will be 
taken, and the lunation will 
be long; if the space be near 
perigee, the moon moves rap- 
idly, and the lunation will be 
short. Moreover, the motion 
of the earth in its orbit is not 
uniform, and the arc AB varies 
in length, which will also 

cause variation in the lunation ; these two causes may partially 
counteract, or may assist, each other. 

331. The moon moves about the sun as well as 
about the earth. — The moon obeys the attractions of both 
the earth and the sun. Were the earth instantly blotted from 
existence, the moon would continue to move about the sun 
in an orbit resulting from the forward motion of the moon, 
modified by the sun's attraction. 

332. The moon's path is always curved toward 
the sun. — Let AB represent part of the earth's orbit, and 
let 1, 2, 3, etc., represent successive positions of the earth 



Fig. 109. 




Fig. no. 



and moon, the small circles showing the moon's orbit. It is 
evident that while the moon revolves about the earth, even 



176 



ELEMENTS OF ASTRONOMY 



in the part of its motion which is nearest the sun, it is always 
beyond the straight line which connects A and B, and follows 
a line which is always curved toward the sun. Its deviations 
from the earth's path amount to only about -g^-g part of the 
radius of the earth's orbit. 

THE SUN'S ATTRACTION. 

333. Its effect on the eccentricity of the moon's 
orbit. — Were the moon influenced by no other attraction 





© 



Fig. 112. 



than that of the earth, the line of apsides would point 
always to some fixed point in the heavens, as the earth's 
axis is directed to the pole star. Now suppose the moon's 
orbit in such a position that the line of apsides is di- 
rected toward the sun. As the moon passes opposition, the 
force of the sun is added to that of the earth, drawing the 
moon more forcibly toward the center, and increasing its 
speed. As the moon approaches conjunction, the force of 



THE SUN'S ATTRACTION. 



177 



the sun diminishes that of the earth, and the moon does not 
turn about as soon as it otherwise would. The action in 
either case makes the moon's orbit narrower and longer — 
more eccentric. 

334. Conversely. — A few months later, the line of 
apsides coincides with the quadratures; the attraction of the 
sun no longer assists the radial force, but acts at right angles 
to that of the earth; the moon as it passes apogee or perigee, 
begins to turn sooner, and makes its path more nearly cir- 
cular — the eccentricity is diminished. (Fig. 112.) Hence, 
it appears that the moon's orbit is one of variable eccentricity, 
and that the cause is continually correcting itself. 

335. On the position of the line of apsides. — In 

some positions, one of which is illustrated in the diagram, 
the attraction of the sun being at 

right angles to that of the earth, the ., _^ 

earth can not pull the moon into 
place, causing it to turn about, 
quite as soon as it should; and the 
place of perigee, instead of being 
at M l , as at the last passage, goes 
on to M' 1 ; a new line of apsides is 
thus fixed, a little turned from its 
former place. Under other circum- 
stances, the opposite effect is pro- 
duced, but the forward are greater 
than the backward movements. The 
line of apsides makes a complete 
revolution in about nine years. 

336. On the position of the line of nodes. — Defi- 
nitions. — Daily observations of the moon's right ascension 
and declination, traced upon a celestial globe (108), show the 
moon's path is alternately north and south o( the ecliptic, 

departing as much as 5 degrees (5 (/). Hence, it appears 

that the plane of the moon's orbit is inclined to that of the 
Ast.— ia. 




<*> 



Fig. 



i 7 8 



ELEMENTS OF ASTRONOMY. 




DESCENDING NODE 



e ASCENDING NODE 
Fig. 114. 



earth by such ?.n amount. The points where the moon's 
orbit passes through the plane of the ecliptic are called 
its nodes; that where the moon goes from south to north is 
the ascending node ; the opposite, the descending node. The 

line which joins these points, 
passing, of course, through 
the earth, is the line of nodes. 
337. The nodes move 
backward. — Whenever 
the moon is out of the plane 
of the ecliptic, the sun tends 
to draw it back into that 
plane. As the moon ap- 
proaches the node nearest 
the sun on the line AN, the 
sun does not allow it to pass 
on to N, but draws it in to 
the ecliptic a little sooner at 
N 1 , and causes it to cross 
at a somewhat greater angle. Immediately after the passage, 
as the moon is moving away on the new line, the attraction 
of the sun still draws it 
back toward the eclip- 
tic, and restores the path 
to the same angle that 
it had before, bringing 
the moon into the line 
N 2 B, parallel to the 
first line AN. The re- 
sult of the whole action 

is to move the node from iVback to N 2 , while the obliquity 
of the orbit is left unchanged. The moon's path is repre- 
sented by the slightly curved dotted line. At the node 
farthest from the sun this effect is reversed ; but because the 
sun is farther from the moon by the diameter of the moon's 
orbit, the effect is not so great as at the nearest node. 




ECLIPTIC 



Fig. nf 



THE SUN'S ATTRACTION. 



179 



Hence, the line of nodes moves slowly backward, and com- 
pletes a revolution in about 19 years (18.6 y.). 

338. Results. — The moon's motion is, therefore, a com- 
bination of these several elements: 

1. Its revolution about the earth. 

2. Its revolution about the sun. 

3. The vibrating eccentricity of its orbit. 

4. The slow direct rotation of the line of apsides. 

5. The slow retrograde rotation of the line of nodes. 
Besides these, there are minor perturbations caused by the 

attraction of the planets at varying distances. 

339. Illustration. — An idea of these several motions 
may be rudely realized thus : 




Fig. 116. 



Cut an ellipse from stiff paper or card-board; thrust a pen- 
cil through one of the foci, in the place of the earth ; conceive 
the moon to move round the edge of the card, and that the 
card itself slightly expands in length and contracts in breadth, 
and vice versa. Hold the pencil obliquely, that the position 
of the card may represent the obliquity o( the orbit. ruin 
the pencil in the lingers, slowly, Opposite to the motion oi' the 
hands of a watch, and we have the motion oi the apsides. 
Hold the lower end of the pencil Stationary, and make the 
upper end describe a circle slowly, in the same direction as 



i8o 



ELEMENTS OF ASTRONOMY. 



the hands of a watch, always preserving the same angle of 
inclination, and we have the motion of the line of nodes. 
Make all these motions together while walking about some 
fixed point to represent the sun ; we find that the motion of 
the moon, though intricate, may be followed and compre- 
hended. 

PHASES. 

340. The phases of the moon. — The new moon in 
the west shows a narrow crescent, its convex side toward the 




Fig. 117. 



sun. As the moon grows older the crescent widens, and 
when it rises in the east as the sun sets in the west, its face 



PHASES. 181 

is full and round. It then diminishes as it had increased, 
showing at last a narrow crescent in the east, shortly before 
sunrise, the convex side still being toward the sun. Between 
the time of old and new moon it sometimes passes between 
us and the sun, obscuring the sun's light with a broad black 
disc. These changes are readily understood, when we con- 
sider that the moon is an opaque body, which is bright only 
as it reflects sunshine. When the moon is in conjunction, 
the side on which the sun shines is turned from the earth, 
and the moon can not be seen unless it comes exactly be- 
tween the observer and the sun. At the first octant, the 
half which is visible at the earth includes a part of the half 
which is lighted by the sun, and we see a crescent. At the 
first quarter, half of the visible side includes half of the 
illuminated side. At the full moon, the whole illuminated 
side is turned toward the earth. 

341. The ashy light of the moon. — On the first or 
second clear night after new moon the entire disc may be 
seen; a thin bright crescent is on the side nearest the sun, 
while the rest of the disc shows a pale, ashy light, barely 
discernible. The earth is an opaque body, lighted by the 
sun, and, therefore, presents to the moon a series of phases, 
similar to those which we see in the moon, but in a reverse 
order. When we see new moon, an observer at the moon 
would see "full earth;" but*as the diameter of the earth is 
nearly four times that of the moon, it gives nearly sixteen 
times as much light to the moon as the moon gives us. This 
light, the light of the sun reflected by the earth, is again 
reflected by the moon, and causes the ashy light over the 
otherwise invisible part of the disc-. As the moon grows 
older, the ashy light vanishes in contrast with the more 
brilliant light o( the part illumined by the sun. 

"Late jrestre'en 1 saw the now Moon. 
With the old Moon in her arms." 



1 82 ELEMENTS OF ASTRONOMY. 



IN THE TELESCOPE. 

342. In a telescope of moderate power the moon 
ceases to show a flat disc, but rounds into a beautiful sphere, 
which seems to float in the air. Its surface is roughly irreg- 
ular. Especially about the first quarter, the tenninator, or 
the line which divides the light from the dark part of the 
disc, is very much broken. Bright spots appear a little 
beyond the line ; in a few hours they unite with the light 
portion, and are then followed by dark shadows stretching 
away far from the sunshine. At full moon, these strong 
contrasts vanish, but there is yet a great variety of light and 
shade. 

343. Lunar mountains. — The bright spots are the tops 
of lunar mountains, gilded by the rising sun. As the slow 
rotation of the moon brings the mountains farther into sun- 
shine, the light is seen gradually creeping down their sides, 
and joining that in the valleys below, while the shadows are 
thrown in the opposite direction. These shadows disappear 
under the vertical sun at full moon, and are cast on the 
opposite side of the mountains as the moon wanes. The 
height of the mountains may be estimated from the length 
of the shadows, or from the distance from the terminator at 
which the bright top may be seen (16). The highest have 
an elevation of about 25,000 feet, but little less than that of 
the highest mountains on the earth. 

344. Lunar maps. — Much labor has been expended 
upon maps of the moon's surface, the most accurate, as yet, 
being that of Messrs. Beer and Madler, 30 inches in diam- 
eter. The "Moon Committee" of the British Association 
have parceled the moon out, and are preparing a map 100 
inches in diameter, with all the accuracy of photography. 
The various mountain ranges have been named for ranges 
on the earth; single peaks and craters for eminent astron- 
omers; level portions, under an old supposition, were called 



IN THE TELESCOPE. 



183 



seas and marshes, as Sea of Tranquility, Sea of Nectar, 
Ocean of Tempests, — names entirely fanciful. 

345. Lunar craters. — A peculiar feature of the lunar 
landscape is the great number of rings, walled basins, or 
craters. These appear to be of volcanic origin, if not the 




Fig. 118. — Mountains of the moon ; Copernicus, (Nasmyth.) 



actual craters of volcanoes. Their diameters are very large, 
50, 100, and even i v }^ miles. The walls are steep ami 
ragged, the interior slope often descending much deeper than 
the exterior. As one o\ these craters comes into sunshine, 
the slope opposite the sun is bright with light, while the 
bottom is dark in the shadow of the wall. A volcanic cone 
frequently rises from the bottom ^^ a crater. 



1 84 ELEMENTS OF ASTRONOMY. 

346. Tycho is a remarkable crater near the southern 
edge of the moon. In diagrams, which usually show the 
moon as it appears inverted in a telescope, this mountain ap- 
pears near the top. Its diameter is about 54 miles; its walls 
are 16,000 to 17,000 feet high; a mountain rises from the 




Fig. 119. — Mountains of the moon ; region near Tycho. (Nasmyth.) 

bottom of the crater, about a mile high. The region about 
Tycho is completely broken with ridges, peaks, and craters. 
Tycho is notable for the great number of streaks of light 
which diverge from it in every direction, particularly to the 
north-east. They are so regular that they seem like merid- 
ians, and the mountain appears to be the lunar south pole. 
These bright lines are best seen at the time of full moon; 
they are not ridges, . or they would cast shadows, when the 
sunlight is oblique to them. 



IN THE TELESCOPE. 



"85 



347. Rilles. — These look like huge railway excavations, — 
two parallel slopes on either side of a deep sunken way. 
They are sometimes a mile and a half wide, from 1300 to 
2000 feet deep, and from 10 to 125 miles long. Their 
dimensions, and the fact that they cut through mountain ridges 




Fig. 120. 



and craters, show that they can riot be river beds. Carpenter 
and Nasmyth suggest that the rilles and the radial streaks 
about Tycho, Kepler, Copernicus, and other ring mountains, 

are the marks o\ cracks produced by internal convulsions, 
and illustrate by a photograph (Fig. \ 20) o( a glass ball, 
cracked by the expansion o( water within. 



1 86 ELEMENTS OF ASTRONOMY. 

348. Active volcanoes. — In 1787, Herschel reported 
three active volcanoes in the moon. In 1794, two persons 
in different parts of England saw a bright spot, like a star 
of the third magnitude, upon the dark part of the moon's 
disc, the moon not having reached her first quarter. As the 
moon passed before the star Aldebaran on that evening, 
most astronomers suppose that star to be the spot seen. 

During lunar eclipses bright spots have been seen, which 
were thought to be volcanoes. They have been explained 
as caused by earth-light reflected again from smooth surfaces 
of rock. 

IS THE' MOON INHABITABLE? 

349. Has the moon water? — The gray places were 
first called seas and marshes, names which now seem in- 
appropriate, as no evidence of water can be found. The 
sunlight reflected from sheets of water would reveal effects 
which could be recognized by the polariscope (309), but they 
do not appear. Prof. Mitchel describes a spot which has 
the appearance of a lake. From mountains which surround 
it, a sloping beach extends to the level surface. The 
highest magnifying power shows no roughness, and the shad- 
ing is as regular as if the cavity were filled with ice or 
quicksilver. "This phenomenon," says Prof. Mitchel, "has 
baffled the most diligent and persevering efforts to explain." 

350. Has the moon air? — The absence of twilight; 
the absence of refraction, when the light of a star passes 
near the surface of the moon ; and researches with the polar- 
iscope and spectroscope all indicate that the moon has no 
atmosphere. Without air, the water, if any exists, must be 
in a state of vapor, as water evaporates in a vacuum; but 
there is no evidence of even vapor of water. 

351. Is the moon inhabited? — Without air and water 
no form of vegetable or animal life which we know can exist. 



THE ROTATION OF THE MOON. 187 

Even if these conditions were satisfied, the slow rotation of 
the moon, alternately shutting off the sun's rays, and expos- 
ing plants and animals to their unmitigated fierceness for 
two weeks at once, would require organizations materially 
different from those found on the earth. 

May not the rugged nature of the moon's surface show 
what the condition of our earth would be, without the air 
and water, which have worn down the ridges, filled up the 
chasms left by the earthquake and the volcano, and by a 
long series of geologic changes fitted the earth for the 
habitation of man? 



THE ROTATION OF THE MOON. 

352. The moon always shows the earth the same face, 
with little variation, save that from the changing shadows 
as sunshine comes from different directions. Hence we 
conclude that she turns on her axis once during each revo- 
lution. A person may readily illustrate the rotation of the 
moon by walking about a table, keeping his face always 
turned toward the central object. He will see that he looks 
toward every part of the room, or every point of the com- 
pass, successively, precisely as if he had turned once about 
in one place. The rotation coincides exactly with an average 
revolution. If not, the moon would gradually turn some 
other side to the earth, and ultimately would show her entire 
surface. We now see in the full moon, without a telescope, 
a rude sketch of a face, — eyes, nose, and mouth ; ancient 
writers describe the same appearance. 

353. Librations. — While, in the main, the moon always 
turns the same side toward the earth, she passes in her com- 
plex movements through certain changes oi position, which 
resemble oscillations or vibrations, and. in consequence o\ 
these vibrations, we see occasionally small portions oi the 



1 88 ELEMENTS OF ASTRONOMY. 

opposite face of the moon. These changes are called libra- 
tions. There are three, libration in longitude, libration in 
latitude, and the diurnal libratio?i. 

354. Libration in longitude. — The motion of the moon 
in its orbit is variable; that about its axis is regular. Hence, 
when the moon is in that part of its path where it moves 
slowly, the rotation gets a little in advance, and the moon 
shows a little of the opposite side on the east; in the opposite 
part of the orbit, the rotation does not keep up with the 
orbital motion, and we see a little farther on the west. As 
this is a result of the moon's variable motion in longitude it 
is called lib?'ation in longitude. 

355. Libration in latitude. — The axis of the moon 
makes an angle of about 83*^ degrees with its orbit. Hence, 
in one part of a revolution the north pole is turned toward 
the earth, in another it is turned away from the earth; in 
the first case it is possible to see 63^ degrees beyond the 
north pole; in the second, the same distance beyond the 
south pole. This result is precisely similar to the change of 
seasons as caused by the inclination of the earth's axis to 
its orbit, and to the rays of the sun. It is called libration 
in latitude. 

356. Diurnal libration. — Were the center of the moon's 
visible face always turned exactly toward the center of the 
earth, the visible portion would even then be different to 
persons differently situated on the earth, and the same result 
accompanies the earth's rotation. The observer who sees 
the moon rise, is at the distance of the earth's radius west 
of this central line; when the moon sets, he is at the same 
distance east of that line, and the face turned toward him 
is slightly changed. This variation, of course, occurs every 
day. 

357. From these three librations we obtain some knowl- 
edge of the remote side of the moon ; we can see, at various 



OTHER APPARENT VARIATIONS. 189 

times, about four sevenths of the entire surface. So far as 
we can see, the remote side is not materially different from 
that turned toward us; it has neither the great cavity nor 
the great protuberance which have at times been suggested. 



OTHER APPARENT VARIATIONS. 

358. The moon runs high or low. — The moon is 
never more than 5 9' from the ecliptic (336). In December, 
the sun's meridian point may be as much as 23*^° below 
the equinoctial (53), and, therefore, the midnight meridian 
point of the ecliptic will be 23^° above the equinoctial, or 
for an observer at latitude 40 °, in altitude 50 + 23^° = 
73^°. Hence, if the the full moon at midnight should be 
5 above the ecliptic, its altitude would be 50 -\- 2^)4° Hh 
5 = 78^°. It would then be only n^° from the zenith. 

In June, the full moon at midnight may have an altitude 
as little as 50 — 23 ^4° — 5 = 21 y 2 °. 

It is also evident that the December altitude may be io° 
less, and the June altitude io° more than the numbers above 
found. 



359. Daily delay of moon-rise. — An observer in north 
latitude sees the sun rise earlier, day by day, as it moves 
northward, or as its northern declination increases (136). 
In the same way, motion of the moon north in declination 
tends to make the moon rise earlier. But the daily east- 
ward motion of the moon in its orbit delays its rising, as it 
delays its passage over the meridian (116), by an average 
pf about 54 minutes. If the moon is at the same time nun 
tag northward, that delay may be reduced to 23 minutes ; it' 
southward, it may be increased to 77 minutes; it will rise so 
many minutes later than on the day before. These variations 
occur in some measure during every lunation. 



190 ELEMENTS OF ASTRONOMY. 

360. The Harvest-moon. — The full moon which hap- 
pens nearest the time of autumnal equinox, being in oppo- 
sition to the sun, is near the place of the vernal equinox, 
and at the same time is moving northward. It is, there- 
fore, increasing north declination daily, and, as just explained, 




Fig. 121. 

the daily delay in moon-rise is very small, so that the full 
moon rises for several successive nights with comparatively 
little variation in time. 

Suppose the full moon in September to rise at the point 
1 on a certain day. It will move forward in declination, 
that is, toward the left, and its path will be on or very near 
the ecliptic. At the end of twenty-four hours, it will be at 
the point 2, and will have to pass over only the short dotted 
line from 2 to reach the horizon; its rising will be delayed 
but little. On the third day, its delay in rising will be indi- 
cated by the short dotted line from 3 to the horizon. In 
March, its path will also be near the ecliptic, but in the 
position indicated, and the daily forward motion will bring 
it to the points 2' and 3', from which the longer dotted 
lines indicate much greater delay in rising. 



OTHER APPARENT VARIATIONS. 191 

As the principal harvests in England are completed about 
the time of the September full moon, this has been called 
the Harvest-moon. The next moon has something of the 
same peculiarity, and has been called the Hunter's moon. 

361. Light and heat of moon-light. — The ratio of 
sun-light to that of the full moon is given by — 

Bouguer, at 300,000 to 1. 
Wollaston, at 800,000 to 1. 
Zollner, at 619,000 to 1. 

The latter determination is probably the best. 

Delicate experiments upon high mountains indicate that 
the heat of moon-light, at full moon, is equal to that of an 
ordinary candle at a distance of 15 feet. Even this small 
amount is absorbed by the air before it reaches the earth. 

362. Visibility of small objects on the moon. — The 

distance of the moon is 240,000 miles. A magnifying 
power of 1000 enables us to see the surface as it would 
appear at a distance of 240 miles; a power of 6000 would 
seem to bring the moon within 40 miles. But since light 
is diminished as magnifying power is increased (69), only 
moderate powers can, as yet, be used to advantage in 
studying the moon. 



363. RECAPITULATION. 

The different relative positions of the sun ami earth cause the 
moon to change : 

The time of synodic revolution; 
'I 'lie eccentricity oi~ orbit ; 

The position oi' the line o( apsides; 
The position of the line ol' nodes. 
Phases are seen when the side illuminated l>y the sun is viewed 

from different positions. 



192 ELEMENTS OF ASTRONOMY. 

The ashy light of new moon is the reflection of light received by 
reflection from the earth. 

The telescope shows plains, mountains, craters, rilles, but no evi- 
dence of water, air, or inhabitants. 

Librations show alternately small parts of the moon's farther side. 
Motion in orbit which does not correspond to rotation causes libration 
in longitude; inclination of moon's axis, libration in latitude; the 
place of the observer, alternately east and west of the line which 
joins the centers of the earth and moon, diurnal libration. 




Fig. 122. — Theory of Eclipses. 



F. 193. 



CHAPTER XIV. 



ECLIPSES OF THE MOON. 



364. The earth's shadow. — The earth is an opaque 
body, and, therefore, intercepts all the sunlight which falls 
upon it, leaving a space beyond which is not illuminated. 
In the diagram, the two lines which touch the earth arfd the 
sun, on the same side of each, show the outline of a space 
beyond the earth which is without light; this is the earth's 
shadow. As the sun is larger than the earth, it is evident 




Fig. 123. 



that the lines will meet, if sufficiently prolonged ; hence, it 
appears that the shadow of the earth is a cone, whose base 
is nearly a great circle of the earth. The central line or 
axis of the shadow passes through the centers o( the earth 
and sun, and is, therefore, in the plane o\ the ecliptic, 

365. The dimensions of the shadow.— We find its 
length thus: The corresponding parts o\ the triangles SBA 
and EDA are in proportion ; hence, 

Ast.-I 3 . ^0;^ 



194 



ELEMENTS OF ASTRONOMY. 



SB : ED : : SA : EA ; or, 
433,000 : 4000 : : 93,000,000 -\- x : x, whence 

x = 867,000 miles, or about 3^ times the distance to 
the moon. 

By a similar proportion, the breadth of the shadow at the 
distance of the moon is found to be about 5800 miles, or 
about 2 2 /z times the diameter of the moon. But it must be 
remembered that the distance of the earth from the sun is 
variable, and, therefore, both the length and breadth of the 
earth's shadow vary in proportion. 

366. The moon is 
eclipsed whenever any 
part of its disc is darkened 
by the earth's shadow. If 
the shadow merely touches 
the disc, the contact is 
called an appulse. If the 
shadow covers only part 
of the moon, the eclipse 
is partial; when the moon 
passes entirely into the 
shadow, the eclipse is total. 
Because the shadow is 
# half above and half below 
the plane of the ecliptic, 
it is evident that the moon 
when eclipsed must be 
very near that plane, or, 
very near its node (336); 
and it is also evident that 
the moon must be in oppo- 
sition (261). In Fig. 124 no eclipse occurs, because the 
moon is not in opposition. In Fig. 125 no eclipse occurs, 
because, although the moon is in opposition, it is below the 
plane of the ecliptic, not having yet come to the node. 




Fig. 124. 



ECLIPSES OF THE MOON. 195 

If the moon's orbit lay in the ecliptic, an eclipse would 
occur at every opposition; if the line of nodes moved (336) 
with the syzygies (328), one might never happen. 

As the shadow of the earth is about 5800 miles in diam- 
eter, the moon's surface must pass within about half that 



^^^ OPPOSITION ~ 

Fig. 125. 

distance, 2900 miles, of the central line in order to insure an 
eclipse, and that requires that opposition be within about 
12 of the node. 

367. The earth's penumbra. — The earth's shadow is 
called the umbra. Lines which are tangent to the earth 
and sun (Fig. 123) on opposite sides of each, show the out- 
line of the frustum of a cone, whose smaller base is nearly 
a great circle of the earth, and which stretches away in- 
definitely, in a direction opposite to the sun. This space 
is called the earth's penumbra, or partial shadow. Any 
object in this space loses part of the sun's light, intercepted 
by the earth. When the moon enters this reversed cone 
of partial shadow its light gradually wanes, until the sun's 
rays are quite cut off as the moon enters the (-one o\' total 
shadow. 'Hie penumbra is about 9800 miles broad at the 
moon's distance. 

368. The moon visible when eclipsed.— -Even when 

totally eclipsed, the moon's disc usually shows a dull red or 
coppery light. This can not be caused by sunlight reflected 



196 



ELEMENTS OF ASTRONOMY. 



from the earth, like the ashy light of the new moon (341). 
for the illuminated side of the earth is turned from the moon. 
It comes from rays of sunshine bent about the earth by pass- 
ing through the atmosphere (124). In some cases the red light 
does not appear, and the moon becomes quite invisible; at 





y / ^^ ^^^\ 


\j>0°°^- 




, mi^ : --^m^^tk^~ \ 




ECLIPTIC f L— AS 


. HUM B-- 


ECLIPTIC 


0^^\ly\ 






'^^^^^w^Y 


\J10^^ 


^0^^ 


^L r 





Fig. 126. 



other times the light is very much diminished; the difference 
is due to the state of the air where the bent rays pass the 
earth. 

369. The eclipsed moon has been seen before sunset. 
This would seem to be contrary to the theory of eclipses, 
since it would imply that the three bodies were not in the 
same line, both sun and moon being above the horizon. But 
it will be remembered that all bodies near the horizon are 
elevated by refraction (124), and that for this reason both 
sun and moon are visible when they are actually below the 
plane of the horizon; hence, it has happened that the moon 
rose in eclipse just as the sun was setting. 



ECLIPSES OF THE SUN. 197 

370. Occultations. — The disc of the moon not 
infrequently passes over and hides a star or planet 
which is then said to be occulted. From new to full 
moon the stars disappear at the dark side of the 
disc, as that side is foremost in the moon's motion; 
from full to new, they disappear on the bright side 
and re-appear on the dark side. 

371. Diagrams. — In all astronomical subjects it 
is difficult to show correct relations of size in dia- 
grams, or by apparatus. The figure shows the pro- 
portion of the earth's shadow, the moon just going 
into eclipse. The sun must be understood to be 
represented by a globe 5^ inches in diameter, and 
about 49 feet distant. 

ECLIPSES OF THE SUN. 

372. The moon's shadow. — The moon, like 
the earth, carries on the side opposite the sun, a 
cone of shadow and a conical penumbra. The 
length of the moon's shadow varies with the relative 
position of the two bodies; it averages 231,690 
miles, a little less than the average distance of the 
moon. When the earth is at aphelion and the moon 
at perigee (210) the shadow is long enough to reach 
about 14,500 miles beyond the earth's center, and 
covers a space on the earth about 170 miles in 
diameter. When the earth is at perihelion, and the 
moon at apogee, the shadow docs not reach the 
earth j the earth passes through only the partial 
shade of the penumbra. 

373. Solar eclipse.— A person in the cone of 
shadow sees no part of the sun. To him the sun is 
totally eclipsed, or, to speak more exactly, occulted, F . 

hidden, by the moon. A person in the penumbra 



198 ELEMENTS OF ASTRONOMY. 

will see the moon cover a part of the sun's disc; to him 
the sun is partially eclipsed. When the shadow is not long 
enough to reach the earth, the lines which define it being 
prolonged beyond the apex form a second, reversed cone. 
A person in this cone will see the sun's disc surround the 
moon with a ring of light; the eclipse is annular. If the 
observer is also on the line which joins the centers of the 
sun and moon, that is, on the axis of the moon's shadow, 
the eclipse is annular and central. 

The same eclipse may show all these forms at different 
places, as the shadow of the moon sweeps over the earth's 
surface. The shadow may be long enough to reach the 
surface, but not the center of the earth; then the eclipse 
will be annular to those who see it near sunrise or sunset, 
and total to such as see it near midday. The space in 
which the eclipse is either annular or total is surrounded 
by a belt, of width varying at different occasions, in which 
the eclipse is partial. 

374. Baily's beads. — Most of the phenomena of a solar 
eclipse have been described in the chapter on the sun. As 
the bright thread of light between the dark edge of the 
moon and the edge of the sun vanishes, it is often divided 
into many bright points, called from their first observer, 
Baily's beads. They are thought to be caused by rays of 
sunlight streaming through gaps in the ragged mountain 
ranges of the moon. They will be observed most readily 
at that part of the moon's disc where the mountain chains 
are most broken. 

375. "The intensity of the illumination of the atmosphere 
naturally diminishes during the entire duration of a total 
eclipse, from its commencement until the beginning of its 
totality, to again as gradually recover its primitive intensity. 
This obscurity, during the phase of totality, is, however, far 
from being complete. Thus only the brightest stars, and 
some of those of the second magnitude, are seen. The 



FREQUENCY OF ECLIPSES. 199 

planets, Mercury, Venus, Mars, Jupiter, and Saturn, how- 
ever, have been likewise observed. 

"Terrestrial objects take by degrees a livid hue; they are 
colored with various tints, among which olive-green predomi- 
nates. Orange, yellow, vinous-red, and copper tints, give 
to the landscape a singular appearance, which, joined to 
the very perceptible lowering of the temperature, contributes 
to produce a profound impression on all animated beings." 

376. Rate of motion of the eclipse shadow. — The 

moon moves in its orbit at the rate of about 2080 miles an 
hour, while the surface of the earth at the equator moves, 
in consequence of rotation, 1040 miles an hour, in the same 
direction. Hence, the moon's shadow moves over the sur- 
face of the earth at the equator, 2080 — 1040:= 1040 miles 
an hour. When the axis of the shadow is oblique to the 
surface, or is received at some distance from the equator, 
it moves more rapidly. 



FREQUENCY OF ECLIPSES. 

377. Solar. — A lunation (329) averages 29 d. 12 h. 44 m. 
3 sec. = 29.53 -f- days. There are, therefore, 365.25 -f- 
29.53 = 12.4 lunations in one year. The distance on the 
ecliptic from one conjunction of the sun and moon to the 
next, is 360 -=- 12.4 = 29 . A solar eclipse may occur 
when conjunction is within 18 of the node (App. VII). 
The next conjunction being 29 farther advanced, or 29 — 
i8° = ii° beyond the node, is also within the ecliptic limit, 
and a second solar eclipse occurs. 

The nodes move westward (337), making one revolution 
in 18.6 years, or [8.6 \ 12.4 230.64 lunations; hence, 
their motion is 360 : 230.64 1.5O for one lunation, or 
9.36 for six lunations; hence, the second mule is 180 
<).^c v ' 170.O4 in advance o( the first. Now the seventh 
conjunction will be 6 \ 29° — 17 ,0 



200 ELEMENTS OF ASTRONOMY. 

conjunction, or 174 — 18 == 156 in advance of the first 
node, or 170.64 — 156 = 14. 64 behind the second node. 
But this is within the ecliptic limit, causing a third solar 
eclipse. 

The next, or eighth conjunction, 29 farther on, is 14. 36 
beyond the second node, and causes a fourth solar eclipse. 

The first node, by reason of the backward motion, or pre- 
cession of the nodes, will be found again at 341. 28 from 
its first place; while 12 lunations will carry the 13th, 348 
from the first conjunction, and as the first conjunction was 
18 behind the first node, the 13th will be 348 — i8° = 
330 in advance of the first node, or within 341. 28 — 
330 = 11.28 of the second place of the first node. This 
is again within ecliptic limit, and causes a fifth solar eclipse. 
The 13th conjunction occurs in 12 X 29. 53 days 1=354.36 
days, or about 11 days less than one year; hence, the five 
solar eclipses described may occur within one year. 

378. Lunar. — Two lunar eclipses can not occur in two 
consecutive months, since the lunar ecliptic limits possibly 
extend only 2 X 12 24' = 24 48' in length, while the 
motion of the place of opposition, like that of conjunction, 
is 2 9 in a lunation. The seventh opposition is 6 X 29° = 
1 74 in advance of the first, and as the second node is 
170.64 in advance of the first, the seventh opposition has 
gained 3.36 relatively to the nodes, and may be again within 
the lunar ecliptic limit. 

Thus, if an eclipse of the moon happens at 12 behind 
the first node, a second will occur 12 — 3.36° = 8. 64 
behind the second node, and a third, 5.28 behind the third 
node; and, as the three nodes may all be passed in 346.62 
days, three lunar eclipses may occur in one year. 

379. The number possible in one year. — The place 
of opposition follows that of conjunction in 14. 5 ° on the 
ecliptic. Hence, if a solar eclipse is more than 14.5 — 
12.4° = 2. i° behind the first node, a lunar eclipse may occur 



FREQUENCY OF ECLIPSES. 201 

at the next conjunction, since that will be within the possible 
ecliptic limit. Hence, in the case supposed, in Art. 377, the 
first, third, and fifth solar eclipses will each be followed by a 
lunar eclipse within 15 days. 

As only about eleven' days of the year remain after the 
fifth solar eclipse, there is not time enough for the next lunar 
eclipse to happen within that year. Hence, the greatest 
number of eclipses possible in one year is seven, of which 
jive are solar, and two lunar. 

The least number of eclipses possible in one year is two, 
both of the sun. 

Lunar eclipses are visible to the entire hemisphere turned 
to the moon; solar eclipses are only visible at those places 
on the earth which enter the moon's shadow. Hence, 
although solar eclipses are most numerous, lunar eclipses are 
oftenest seen at any given place. 

380. The Saros. — Eclipses occur only when the sun 
and moon are in conjunction or opposition near one of the 
moon's nodes. Conjunction is repeated at intervals of 29.53 
days; the sun passes the same lunar node at intervals of 
346.62 days. Whenever these intervals end on the same 
day, conjunction will have the same relation to the node 
which it had at first, and an eclipse of the same nature will 
happen. Now, 223 intervals bring a conjunction in 6585.19 
days, and 19 intervals bring the sun to the same node in. 
6585.78 days. But 6585.19 days equal 18 years 10-^ days; 
hence, after that period of time, the cycle of eclipses will 
return again, the eclipses being repeated with the same gen- 
eral characteristics, but some hours later in the daw and. 
therefore, visible at different places. This period, called the 
saros, was known to the ancient Chaldeans, who predicted 
eclipses by it. In it there are usually 41 solar and 29 lunar 
eclipses. It is not perfectly accurate, by reason o\ the 
various disturbing causes which modify the moon's orbit, 
but it serves to direct the attention o\ astronomers to the 
most important eclipses. 



202 ELEMENTS OF ASTRONOMY. 

381. The golden number is not to be confounded with 
the saros. In Pagan and Jewish rituals certain ceremonies 
were to be observed at certain times of the year, and during 
particular phases of the moon. In the Christian church the 
time of Easter is similarly found. Meton discovered that 
235 lunations are completed in 19 years (235 X 29. 53 days = 
6949.55 days, and 19 X 365.2422 days = 6949.6o days); it 
is only necessary to record the dates of one cycle of lunar 
phases for 19 years, to know them for the same days of the 
year during each subsequent period. The Greeks deemed 
this discovery of such importance that they ordered the 
number to be inscribed on their public monuments in let- 
ters of gold. 



382. RECAPITULATION. 

The earth's shadow is a cone about 860,000 miles long, and, at 
the moon's distance, 5800 miles wide ; the penumbra, at the same 
distance, is 9800 miles wide. 

The moon's shadow is about 230,000 miles long; at some times 
more, at others less, than the distance to the earth. 

The moon is totally eclipsed when it passes entirely into the earth's 
umbra ; otherwise, the eclipse is partial. 

An eclipse of the sun is total to a person in the moon's umbra; 
partial to one in the penumbra ; annular to one in the penumbra and 
within the lines of the umbra. 

Eclipses possible in one year : 

Greatest No. Least No 

Solar, 5 2 

Lunar, 3 o 

Both, 5 S + 2 L 2 S 

The Saros ; the time after which eclipses are repeated in similar 

order: 18 years ni days. 

The Golden Number; the time after which the phases occur on 

the same days of the month : 19 years. 



CHAPTER XV. 



THE TIDES. 



383. Definitions. — The alternate rising and falling of the 
waters of the ocean, twice in every lunar day of about 25 
hours, are called tides. The rising water is flood tide, and the 
highest level reached, high water ; the falling water is ebb 
tide, and the lowest level reached, low water. The farthest 
line of the beach which the receding waters at any time dis- 
close, is low-water mark. 

At the time of new and of full moon, high tides are above 
the average, and are called spring tides; at first and last 
quarters, they are below the average, and are called neap 
tides. When high water is highest, low water is lowest, and 
conversely. 

The spring tides are generally from once and a half to 
twice the height of the neap tides. 

384. The tides are caused by the sun and the 
moon. — From the fact that high tide each day follows .it 

rather regular intervals after the passage of the moon over 
the meridian, and that spring and neap tides occur at certain 
phases of the moon, we infer that they are in some way 
connected with the motions o\ that body, and caused In' 
its influence. 

But the tides vary not only at different times o( the month, 
but at different seasons o( the year. They are highest oi all 
at the time of the equinoxes, and high tide is lowest at the 

( »3 ) 



204 ELEMENTS OF ASTRONOMY. 

time of the solstices; the tides of the summer solstice are 
lower than those of the winter solstice. Hence, we infer 
that the sun has also an influence modifying the rising and 
falling of the waters. The ancients understood so much, 
but the nature of the influence was to them unknown. 
Pliny wrote "Causa in sole lunaque ;" the cause is in the 
sun and the moon. 



THE EARTH'S SHAPE AFFECTED, 

385. First, by terrestrial gravitation. — We have 

learned (161) that the earth, if at rest, and influenced only 
by the mutual attraction of its particles, would assume the 
shape of a perfect sphere. Each point on its surface would 
be equidistant from the center, not because the center has 
any peculiar attractive force, but because in this spherical 
shape all the attractions in one direction are exactly counter- 
poised by the attractions in the opposite direction. 

386. Second, by rotation. — We also found that when 
the earth rotates on its axis, the tangential force of the par- 
ticles near the equator, where the motion is most rapid, 
opposes the attraction of the rest of the sphere, or the attrac- 
tion of gravitation; that in some degree the weight of those 
particles is diminished, and, therefore, the shape of the earth 
changes until the longer column of lighter matter at the 
equator is balanced by the shorter column of heavier matter 
near the pole; remembering that the same matter may be 
heavy or light, as it receives more or less attraction. 

E D C B A A 

E D C B A KJ 

Fig. 128. 

387. Third, by an external attraction. — Let A, B, 

C, D, and E, be several particles of matter in a line, and 



THE SHAPE OF THE EARTH. 205 

suppose them attracted by a mass, X, at some distance on 
that line, acting in accordance with the known laws of 
gravitation (158). The nearest particle, A, is drawn more 
than the others; B, next; C, next, and so on, the force on 
each particle being less as the square of its distance from X 
is greater. If there were no opposing force, each particle 
would obey the impulse given to it, and would move at a 
rate proportioned to the force of attraction, A going fastest, 
B, next, and so on. But if other forces oppose, the par- 
ticles will still strive to move, and will be prevented only 
when a part of the opposing force, equal to this external 
attraction, has been exhausted. The effect of the external 
force, in either case, will be to draw the particles away from 
each other, along the line EX, into the new positions A 1 , 
B 1 , etc. That is, their mutual attraction for each other, if 
they have any, will be weakened. 

388. Illustration. — Thus, suppose three boys, John, 
Charles, and Henry, of various strength, join hands and run 
along the street; the strongest naturally goes fastest; the 
weakest, slowest. John, stronger than Charles, will pull 




Fig. 129. 

away from him ; Charles, strongeT than Henry, will do the 
same, but will quite likely complain of Henry for holding 

him back, while, in fact, the little fellow is doing all he can 
to keep up. So, although all are earnestly striving in the 
same direction, the first ami last hoy seem each to be pull- 
ing away from the boy in the middle. 



206 



ELEMENTS OF ASTRONOMY. 



389. Now, let C be the earth's center, and A and B, two 
particles at opposite ends of a diameter which points toward 
some external attracting force, say the moon, M. Their 
mutual attraction is weakened by the external unequal at- 
traction of the moon. But the mutual attractions of P and 
R, on a line perpendicular to AB are not diminished, since 





-M 



Fig. 130. 



they are equally distant from the moon. In fact, as they 
are outside the central line of the moon's force, it tends to 
draw them into that line, and, hence, to increase their 
mutual attraction. The same is true of all the particles in 
the circle PR, which is perpendicular to the line AB. Now, 
as AB is prolonged, becoming A'B r , and PR is contracted, 
becoming the circle P'R', the shape of the earth becomes 
elongated, or melon-shaped, a prolate spheroid. 

390. The place of the center is not changed, because 
the motion of the moon, in its path, keeps the distance 
between the two bodies the same. Hence, as the position 
of the center is not disturbed, and the diameter of the earth 
has been prolonged, it follows, paradoxical as it may seem, 
that the attraction of the moon upon the mass of the earth 
has forced B farther from the center. In the same way the 
waters are heaped up on the side opposite to the moon as 
well as on that next to it. 

391. The sun's attraction produces a similar effect. 
But it must be remembered that the effect in the case of the 



VARIATION OF TIDES. 



207 



moon is not due so much to the absolute amount of the 
moon's attraction, as to the fact that the attraction is greater 
on one side than on the other, owing to the relatively greater 
distance. The sun's distance from the 
opposite side of the earth, although 
greater, is not relatively as much 
larger, as in the case of the moon, 
and, hence, the difference of the at- 
tractions is not as great. The force 
of the sun to raise a tide is to that 
of the moon in about the ratio of 2 
to 5. 




VARIATION OF TIDES. 



392. Spring tides and neap 
tides. — At new moon, the sun and 
moon, being on the same side of the 
earth, act in concert. At full moon, 
although they act in opposite direc- 
tions, each tends to elongate the same 
diameter of the earth ; hence, the re- 
sults of the attractions are combined, 
and the direct tide of each assists the 
opposite tide of the other. In either 
case spring tides result (Fig. 131). 

At the quarters, the moon's high 
water is in the place of the sun's 
low water; each draws down the tide 
of the other, and neap tides result 
(Fig. 132). 

When both sun and moon are north 
of the equinoctial, as in our summer, 
the highest part o( the direct tide- 
wave is north of the equator, and 
o\~ the opposite tide wave, south ()( the equatoi 






Fig. 131. 



208 ELEMENTS OF ASTRONOMY. 

winter, the converse is true. Hence, in summer the spring 
tide of the day is higher than that of the night following. 

Highest tides occur when both bodies are near the equi- 
noctial; hence, the extreme height of the tides at the time 
of the equinoxes. 





Fig. 132. 

393. Inertia delays the tide. — Considering the lunar 
tide by itself, we look for high water directly under the 
moon, or, at the place where the moon is on the meridian ; 
as one meridian after another passes the moon in the daily 
rotation of the earth, the tide-wave should move westwardly 
round the earth. But on account of inertia the water can 
not instantly obey the moon's force, and, therefore, high 
water follows a few hours after the moon's culmination, the 
time varying at different ports with the peculiar circumstances 
of the location. The time which regularly elapses at any 
place, between the moon's culmination and the time of high 
water, is called the establishment of the port. 

Lines drawn on the map through the various points which 
are reached by the tide at the same hour, are called co-tidal 
lines. 

It must not be supposed that the water moves about the 
earth ; only the rising, or the wave, moves. Shake a carpet 



VARIATION OF TIDES. 209 

on the ground ; a series of swells and depressions runs from 
the hands through the cloth and vanishes at the farther side. 
The waves run through the carpet; the cloth moves up and 
down, but does not move forward. 

394. Priming and lagging of the tide. — When the 
solar and lunar tide-waves are near each other, high water 
coincides with neither, but falls between the two. Hence, 
if the lunar tide follows the solar, as happens just after new 
or full moon, high water comes a little earlier than the usual 
time fixed by the establishment of the port; if the lunar tide 
precedes, as just before new or full moon, high water is 
delayed, or lags. 

395. Origin and motion of the tide-wave. — The 

tide-wave begins in the great Pacific Ocean. Its general 
course is westward, its rate varying with the breadth and 
depth of the water which it traverses. Its velocity is re- 
tarded in narrow and in shallow places. It enters the Atlan- 
tic at the Cape of Good Hope, and follows the winding 
channel northward until it is turned eastwardly at the Banks 
of Newfoundland and Labrador, and is expended on the 
north-west coasts of Europe. Beginning near South America, 
the tide reaches 

Kamtchatka, in 10 hours. 

New Zealand, " 12 

Cape of Good Hope, " 29 " 

United States, " 40 " 

Western Ireland, ki 44 

London, " 66 

The time from Western Ireland to London is used in 
(lowing round the north coast of Scotland, south through 
the North Sea, and up the Thames. 

396. Height of tides. At the islands of the Atlantic 
and Pacific oceans the average height o( the tide is only 

Ast. — IA. 



210 ELEMENTS OF ASTRONOMY. 

about ^y 2 feet. On the west coast of South America it is 
2 feet. As the wave approaches the east coast of Asia, 
where the depth diminishes, it finds less room to move in, 
and, therefore, rises higher, — not less than 4 or 5 feet. 

A wave which enters a bay through a narrow opening is 
spread over the wider space beyond, and may entirely 
vanish; hence, the oceanic tide produces no effect in the 
Mediterranean Sea. If the wave flows by a broad channel 
into a bay whose breadth constantly contracts, or into the 
estuary of a river, the want of width will cause an increased 
height. The tide rises at 

Long Island Sound, East end, 2 feet 

" " " West end, 7 

Mouth of St. Lawrence, 9 

Quebec, 20 

Boston, 10 

Bay of Fundy, entrance, 18 

" " head of bay, 70 

The great tide-waves of the ocean are called primitive 
tides ; those which run from them up bays, estuaries, and 
rivers, are derivative tides. 

The motion of a tide-wave up a river is necessarily slow, 
as it is delayed by the shallow water, by the narrow chan- 
nel, and by the opposing current. The tide flows from New 
York to Albany in about 9 hours, moving at the rate of 16 
miles an hour. 

397. Local tides. — As remarked, the oceanic tide does 
not enter the Mediterranean ; it has a tide of its own, how- 
ever, averaging about \]/ 2 feet. The length of the sea, 2400 
miles, is about one third the diameter of the earth, and its 
tide is about one third that of the ocean. 

The tides in the Great Lakes are too small to be easily 
observed. A series of observations at Chicago, indicate a 



INFLUENCE ON THE WEATHER. 211 

tide of 1^ inches, about 30 minutes after the moon's cul- 
mination. Here, also, the height of the tide is to that of the 
oceanic tide, as the length of the lake is to the diameter 
of the earth. 



DOES THE MOON INFLUENCE THE WEATHER? 

398. Tides in the air. — As the air is material, it should 
obey the moon's attraction as well as the water. But the air 
flows in no narrowing channels or estuaries like those which 
condense the oceanic tide ; whatever wave it has must be 
compared with the lowest tide-wave in the open sea. The 
only evidence of an aerial tide will be derived from the 
varied pressure of the air, as indicated by the barometer. 
But the tide exists only to restore the balance of pressure 
which has been disturbed by an external attraction. The 
longer column of air under the moon at high tide should not 
press more heavily than the shorter column at low tide, 
because it is precisely the lifting power of the moon which 
causes any difference in height. As we should expect, there- 
fore, the change in the mercury of the barometer due to the 
aerial tide is very slight, if any, — less than .001 of an inch. 

399. Influence of the moon on clouds. — An opinion 
prevails to some extent that moonlight disperses clouds : 
sailors say "the moon eats the clouds." The opinion may 
be defended. The full moon reflects a little solar heat, 
which may have a slight effect to expand vapor, and dissi- 
pate clouds. 

400. Influence of the moon on rain. — Observations 
continued during 28 years, in and near Munich, in Germany, 
gave the number of rainy days in the growing, to the number 

in the waning, moon, as 845 is to 696, or as 6 is to 5. nearly. 
This would indicate that it rains ofienest in the first half o\ 
the month. Similar results were obtained at Paris. Obser 
rations made for 10 years, at Montpcllicr. in the south of 



212 ELEMENTS OF ASTRONOMY. 

France, found 9 rainy days in the growing moon to 11 in 
the waning moon, a result opposite that found at Munich, 
only about 300 miles distant. The results in either case in- 
dicate coincidences, not consequences. More proof is needed 
before it can be admitted that the moon influences rain. 

401. Wet and dry moon. — Equally valueless is the 
tradition that the crescent of the new moon, when nearly 
horizontal, foretells a dry month; or, when nearly vertical, 
a wet month. As with most "signs," those who accept 
them do so from coincidences observed; cases which prove 
the sign are noted; those which do not, are neglected; we 
are convinced because we wish to be convinced. The nearly 
horizontal crescent happens whenever the plane of the moon's 
orbit is in such a position as to carry the moon past conjunc- 
tion above the sun; the vertical crescent in the opposite case; 
the changes from one to another are slow and gradual. 
There can be nothing in either to affect temperature, or 
moisture; that is, to cause, or prevent, rain. 

402. Influence of the moon's changes on changes 
of the weather. — As before, the records of the few reliable 
series of observations give contradictory results. At Vienna, 

100 new moons gave 58 changes of weather. 
100 full moons, 6$ " " 

100 of each quarter, 63 " " 

This indicates that the new moon brings fewest changes 
of weather, which is contrary to tradition. 

Toaldo, at Venice, found that six new moons out of every 
seven brought changes of weather, but he included any 
change which happened within two days, either before or 
after the day, of new moon, actually counting five days. 
Had he added another day on each side, his results would 
have been still more striking, for more changes are likely to 
occur in seven days than in five. In the changeable climate 
of the temperate zone, we can not count on changeless 



RE CAP/TULA TION. 2 1 3 

weather for five days together at any time of year, and if we 
were to select any five days of the month for observations, 
we should find a majority bring change. 

All scientific investigation indicates that the moon has no 
influence on the weather, and that no forecast can be made 
by it. 

The traditions which teach the time of the moon in which 
to sow, to plant, to kill pork, to cut timber, etc., are all too 
absurd to be refuted. 



403. RECAPITULATION. 

Influenced by terrestrial gravitation alone, the earth would be an 
exact sphere ; rotation added, shortens the polar diameter, making the 
sphere oblate ; an external attraction lengthens the diameter which has 
the direction of that attraction, and tends to make the sphere prolate. 

Tides are caused by the attractions of the snn and moon acting with 
forces in the ratio of 2 to 5 ; acting in the same line, they cause spring 
tides ; at right angles, neap tides. 

Tides originate in the Pacific Ocean ; they pass through the Indian 
to the Atlantic Ocean in about 30 hours. 

The height varies inversely as the amount of sea-room from 2 to 
70 feet. Large inclosed bodies of water have local tides. 

There is no evidence of tides in the air, or that the changing moon 
influences rain or the weather. 



CHAPTER XVI, 



THE PLANETS. 



404. Is there a planet between Mercury and the sun? 
The possibility was first suggested by Leverrier. He thought 
that the attraction of such a body might be the cause of cer- 
tain known irregularities in the motions of Mercury. On a 
few occasions observers have reported the passage of a dark 
body before the sun's disc, which might perhaps be such a 
planet. During solar eclipses such bodies have been eagerly 
sought. In that of 1878, Watson reported that he had seen 
two small planets quite near the sun. 

Although for more than forty years the sun has been an 
object of assiduous and most careful study, by methods which 
could scarcely fail of detecting such bodies, none of the sup- 
posed observations have ever been verified. Watson's objects 
were probably stars known to be near the places he assigned 
to them. It is not now believed that any bodies exist be- 
tween the orbit of Mercury and the sun, worthy to be dignified 
with the name planet. 

MERCURY. 
SIGN $ , REPRESENTING A WAND. 

405. Visibility. — This planet is rarely seen without a 

telescope, because it never departs more than 29 from the 

sun. Copernicus mourned that he should go down to his 

tomb, having never seen it. The Egyptians knew it; the 
(214) 



MERCURY. 215 

Greeks called it Apollo, when visible in the morning, and, at 
night, Mercury, the god of thieves. At its greatest elonga- 
tion (270), it may sometimes be seen for about fifteen minutes, 
about three quarters of an hour after sunset, or shortly before 
sunrise, appearing like a star of the fifth to the third magni- 
tude (514). It may be seen for a few days before and after 
the following dates in 1885: April 8, Aug. 1, Dec. 1. The 
dates for subsequent years may be found by subtracting 18 
days per year from those given; thus, in 1886, we find July 
14; in 1887, June 28, etc. 

In the telescope, Mercury shows phases like the moon, 
whence we conclude that it shines by reflecting the light 




Fi &- I33-— Phases of Mercury. 



of the sun. It is most brilliant when near its greatest elonga- 
tion; at superior conjunction, although the whole illuminated 
disc is turned toward the earth, distance makes the disc small; 
near inferior conjunction, only a narrow line of light is shown 
to the earth; in either case, its light is overpowered by the 
light of the sun. 

406. The orbit of Mercury. — The greatest distance 
from the sun may be found from the greatest elongation (2 70) 
to be 43,300,000. 

The sidereal period has been found to be nearly 88 days 
(268). By Kepler's third law (274), 

365 '., - : 88 a :: o; v ooo,ooo ;? : 3(>,ooo,ooo ; \ the cube of 
the mean distance from the sun. 



2l6 



ELEMENTS OF ASTRONOMY. 



43>3 00 > 000 — 36,000,000 = 7,300,000, the eccentricity in 
miles = o. 206 of the mean radius vector. Hence, the least 
radius vector = 28,700,000 miles. 

The eccentricity of Mercury's orbit is much greater than 
that of any other principal planet. 




♦•••♦ 



Fig- 134- 



The plane of the orbit makes an angle of about 7 (7 o' 
7.7") with the plane of the ecliptic. 

The planet's average velocity in its orbit is 29.55 niiles per 
second. 

407. Transits of Mercury are governed by laws pre- 
cisely similar to those which control eclipses of the sun. 
They can occur only when the sun, Mercury, and the earth 
are in the same straight line; that is, when the planet comes 
to inferior conjunction near one of its nodes. 

The sun passes the ascending node about the 4th of May, 
and the descending node about the 7th of November; tran- 
sits must, therefore, occur near one of these days. 

As the angle of the node is 7 , and the sun's apparent 
radius is 16', the limits in longitude of a transit are about 
2 (App. VII). 



MERCURY. 217 

A synodic revolution occupies about 116 days (273), and 
in that time the sun appears to traverse (266) 116 X 0.9856 = 
1 14. 5 . If, then, we inquire if a transit will be repeated in 
3 years, for example, we find that in three years the sun will 
have traversed 3 X 360 = 1080 . 1080 -f- 114.5 = 9 -f 
a remainder of 49. 5 ; hence, the node is 49. 5 ° beyond the 
9th conjunction, and a transit can not occur. 

In 6 years the node is within 15. 5 ° of the 19th conjunc- 
tion, but because Mercury's orbit is very eccentric, its rate 
of motion is quite variable, and the time of a synodic revo- 
lution may at times be considerably less than 116 days; 
hence, the small arc of 15. 5 ° may disappear, and the con- 
junction may be near enough to the node to cause a transit. 

7 and 13 years are periods at which the two points coincide 
most nearly, and, therefore, are most likely to bring transits 
of Mercury at the same node ; on account of the variation 
in the time of the synodic revolution, even these can not be 
relied upon, except after more intricate and exact com- 
putation. In 217 years the entire round of changes is com- 
plete, and the transits recur in regular order. The next 
transits occur May 9, 1891; November 10, 1894. 

408. Shape, size, and rotation. — The most careful 
observations fail to detect any flattening at the poles of this 
planet. Its horizontal parallax, computed from its distance 
(284), and its apparent diameter, give its real diameter about 
3000 miles, or about three eighths that of the earth. When 
compared with the earth, its volume is about .054; its mass, 
.065; its density, 1.21. 

409. Physical constitution.— Because this planet is so 
near the sun, it is observed with great difficulty. The state- 
ments of the older observers are not substantiated by those 
who use the perfected instruments o{ the present day. 
Schroter gave the time o( rotation at 24 h. 5 m., but this 
is not confirmed. [f it be true, the planet's year has about 
86 solar days. 



218 ELEMENTS OF ASTRONOMY. 

Measures of the light of Mercury at its various phases 
have led Zollner to conclude that there is no air present 
sufficiently dense to reflect sunlight. 

The intensity of solar light and heat, endured at Mercury, 
varies with its varying distance from the sun, averaging 
nearly 7 times that received at the earth. At aphelion this 
amount is reduced to 4^, and at perihelion increased to 10 
times. 



VENUS. 
SIGN 9 , A MIRROR. 

410. Appearance. — The appearance of Venus, both in 
and without the telescope, its alternate shining as morning 
and evening star, its phases, and its transits, have already 




Fig. 135. — Phases of Venus. 

been described (252). When most brilliant, it is about 40 
from the sun. At inferior conjunction, though nearest the 
earth, its illuminated face is turned from the earth ; at supe- 
rior conjunction, its light is diminished by its great distance. 
Once in eight years, its position relative to the earth and the 



VENUS. 219 

sun is such as to cause a maximum of brightness; at such 
times it occasionally casts a sensible shadow at night, and 
may be seen during full sunshine. 

411. Orbit. — The dimensions of the orbit may be com- 
puted, as in Art. 270; the greatest elongation being 47^2°. 
The mean radius is 67 millions of miles; eccentricity, 
450,000 miles, or .0068 of the mean radius, showing that 
the orbit is nearly circular. The plane of the orbit makes 
an angle of about 3^5° (3 23' 35") with the plane of the 
ecliptic. The synodic revolution is completed in 583.9 days; 
the sidereal, in 224.7 days. The rate of motion in the orbit 
is 21.61 miles per second. 

412. Transits of Venus are specially important for de- 
termining the solar parallax (277-281). As the nodes are 
75^° an d 255^3° from the vernal equinox, the sun passes 
those points early in June and December, and transits must 
occur in those months. The intervals between transits may 
be found as in Art. 406 ; or, thus : 

The earth, or the sun apparently, passes the same node at 
intervals of 365^ days; Venus, at intervals of 224.7 days. 
Eight revolutions of the earth are completed in 2922 days, 
and thirteen of Venus in 2921. 1 days; at the end of eight 
years, the two bodies will pass the same point within 24 
hours, and may cause a transit. 235 years of the earth coin- 
cide still more nearly with 382 years of Venus; and if a 
transit should not happen at the end of 235 years, one will 



or 1 1 



be quite sure to occur eight years later. In 105 

years after a transit at one node, another may be expected 

at the opposite node. 

Transits of Wains were observed December 4. 1639; June 
5. 1761; June 3, 1769; December 9. 1 S 7 4 ; Pec-ember 0. 
1882. The next transits will occur June S, 2004; June 0. 
201 2. 

413. Dimensions of Venus. Its diameter (283) is 

about 7700 miles, not much less than that of the earth. No 



220 



ELEMENTS OF ASTRONOMY. 



polar compression has been observed. The diameter is not 
easily measured on account of what is called the irradiation. 
If two circles of the same size are drawn, the one white on 
a black ground, the other black on a white ground, the white 




Fig. 136. — Effect of Irradiation. 



circle will appear the larger, and the effect will increase with 
brilliancy of the white circle. The brightness of Venus 
produces this effect. 

414. Rotation. — So lately as 1842, De Vico thought that 
he had determined the rotation by observing the motion of 
irregularities in its surface, and reported a sidereal day of 23 
h. 21 m. 23 sec, of which 231 would complete one of the 
planet's years. Its mean solar day would then have 23 h. 
27 m. 28 sec. of terrestrial time, or 32^ minutes less than 
one of our days. It is now doubtful if the rotation has ever 
been observed. 

415. Atmosphere. — When Venus is nearly between us 
and the sun, the fine crescent on the side next to the sun 
seems to be continued in a complete thin circle of light about 
the whole disc. This can be explained only by supposing 
that the light has been refracted by an atmosphere. A sim- 
ilar effect has been seen at the time of a transit, and when 
the dark side of the planet is turned toward the earth as it is 
passing the node. The atmosphere is thought to be some- 
what denser than that of the earth. Some observers believe 



THE EA R TH, VTE WED ASTR ON O MIC A LLY. 221 

that the atmosphere is filled with dense clouds; others, 
that white patches have been seen near the supposed place 
of the planet's poles, such as will be described for the 
planet Mars. 

416. A Satellite. — Its existence has been affirmed and 
denied. Several observers claim to have seen a small, bright 
crescent near the planet, and have even computed its size, 
volume, and time of revolution. The best modern observers 
can not find it, and insist that those who reported it were 
deceived by reflections of the planet from the surfaces of the 
lenses Of the telescope. Such appearances are known to 
observers as "ghosts," and are troublesome to the inexpe- 
rienced. A satellite might show itself at the time of a transit, 
if it were near enough to the planet to be projected upon the 
sun's disc at the same time. 



THE EARTH, VIEWED ASTRONOMICALLY. 
SIGN ®, A CIRCLE CROSSED BY EQUATOR AND MERIDIAN. 

417. An observer looking from without upon the solar 
system, as upon a vast machine, would see a planet, nearly 
8000 miles in diameter, revolving next beyond the orbits of 
Mercury and Venus, in an elliptical orbit, at a mean distance 
from the sun of 93 millions of miles, and at a rate of 18.38 
miles a second; rotating once in a little less than 24 hours; 
its axis at an angle of 66^° with the plane of its orbit; 
shining by reflected light; its surface showing the hue of 
water, broken by the outlines of two great, and many smaller, 
masses of land, often rugged with mountains and volcanoes; 
its poles surrounded with spares o( white, which increase 
and wane as they are turned from or toward the sun; in 
closed in an atmosphere, in which clouds often obscure the 
lines beneath; and accompanied by a satellite. This planet 
is the Earth. 



222 



ELEMENTS OF ASTRONOMY. 



Although the inhabitants long deemed it the central body 
in the universe, this observer sees that it is neither the largest 
nor the noblest member of the solar family; a family whose 
sun itself, the grandest object therein, is but an inferior mem- 
ber of the magnificent group of suns which occupy, each in 
solitary majesty, a place in that part of the universe within 
the scope of his vision. 

"What is man that thou art mindful of him?" 



MARS. 

SIGN % , A SHIELD AND SPEAR. 

418. Appearance. — To the naked eye Mars is the reddest 
star of the sky, shining with a steady brightness, which varies 




Telescopic views of Mars ; perihelion. 




Fig. 137. — Views in aphelion. 



with its distance from the earth. In the telescope its color is 
less intense, and is relieved by spots of bluish green or white. 
The red portions are thought to be land, showing the general 
color of rocks and soil; the green tints are believed to come 



MARS. 



223 



from water. Definite outlines of lands and seas are discern- 
ible. Mr. Dawes has mapped them, and they have received 
the names of distinguished astronomers, who have given 
special study to this planet. The long, bottle-shaped seas, 




Fig. 138. 



and the vast length of coast-line contrast strongly with the 
broad oceans and compact continents on the earth. 

419. Rotation. — The movement of the spots indicates 
the rotation of the planet in 24 h. 37 m. 22.7 sec. about an 
axis inclined 63. ° to the plane of its orbit. The solar day is 
24 h. 39 m. 35 sec. 

420. As the axis has an inclination not much different 
from that of the earth, the seasons must vary in a similar 
manner (211-224). White spots, brighter than the rest of 
the disc, appear about the poles; when a pole is turned 
toward the sun, the spot about it diminishes, while the oppo 
site one increases, and conversely. In [837, during winter 
at the south pole of Mars, the whiteness extended 35°; in 
1830, in summer at the same pole, the spot reached Only 5 
or 6 degrees from the pole. These facts lead us to suppose 

that the whiteness is reflected from snow and ice which 

gather and melt away as on the earth. Heme, we inter 



224 ELEMENTS OF ASTRfr N0M y^ 

that Mars has water, an atmosph^ e? and var i at ions of climate 
like our own. The varying clearness of outlines, as seen 
near the center of the di^ or at the edge? als0 indicates the 
presence of an atmosT^gj.^ wnue occasionally the whole disc, 
or a part of it, se£ ms t0 b e obscured by clouds. 

421. Orjjjt. — The mean radius of the orbit is about 142 
millions f miles, with an eccentricity of about 13 millions, 
or 9.093. I n 1S77, Mars came to opposition when near its 
perihelion, while the earth was near aphelion; the distance 
between the two bodies was nearly a minimum, about 35 
millions of miles. If these conditions are reversed, Mars 
coming to opposition near its aphelion, when the earth is near 
its perihelion, the distance between the planets will be about 
62 millions of miles. Evidently the first case will be most 
favorable for observations. The next oppositions will occur 
in March, 1886, April, 1888, and May, 1890, etc. 

The planet moves at a mean rate of about 15 miles a 
second, and traverses its orbit in a little less than 2 of our 
years (687 days) ; during that time it makes 669^3 rotations, 
and it has, therefore, 668^ solar days in its year. 

Its orbit makes with the ecliptic an angle of about 2 
(i° 5-')- 

Its diameter is about 4200 miles. The polar diameter is 
shorter than the equatorial by an amount not accurately 
determined. 

422. Satellites. — At the near approach to the earth, in 
1877, Mars was carefully studied by Hall, using the great 
Washington refractor. On the night of August 11, he dis- 
covered, in the vicinity of the planet, a small object, which 
later examination proved to be a satellite. On the night of 
the 1 8th, a second satellite was seen. The newly discovered 
bodies were named Deimos and Phobos. They are by far 
the smallest heavenly bodies yet known. Their data are as 
follows : 



RECAPITULA TION. 



225 



Name. 


Mean Distance. 


Period of 
Revolution. 


Diameter. 

Miles. 


Mars' Dia. 


Miles. 


Phobos 
Deimos 


1-39 
3-48 


5820 
I460O 


7 h. 39 m. 
30 h. 17.9 m. 


5 to 20 

IO to 40 



Phobos is remarkable because its time of revolution is 
less than one third the planet's day. It is the only instance 
known in which the time of revolution of a satellite is less 
than the time of rotation of its primary. 



423. 



RECAPITULATION OF INNER GROUP. 



The four planets, Mercury, Venus, Earth, Mars, form what is called 
the inner group. A comparison of more important items shows many 
points of similarity, with occasional differences. 

In size, Venus and Earth nearly agree ; Mercury is a little less, 
Mars a little more, than half as large. 

In inclination of axis, Mars agrees with Earth. 

In time of rotation, and consequent length of day, so far as known, 
all show a remarkable coincidence. 

Venus, Earth, and Mars have each an atmosphere^ hence twilight; 
all shine by reflected light, hence show phases. 

Mars is probably diversified by seas and continents like Earth. 

Earth has one satellite; Mars has two. 



Diameter in miles, 
Inclin. of axis. 
Solar day, 
Mean distance from 
Sun, in millions of m. 

Velocity in orbit, m. 



Mercury. 


W'lllls. 


Earth. 


Mars. 


3OOO 


7700 


7913 


4200 






66$° 


"3° 


23 1 


. 27', m.(?) 


24 h. 


24 h. 39J m 


36 


07 


93 


142 


29.6 


21.6 


18.4 


15- 



Ast. 



CHAPTER XVII. 

THE MINOR PLANETS. 

424. The space between Mars and Jupiter. — As 

soon as the planetary distances were determined, astronomers 
saw that as far as to the orbit of Mars, distances increase in a 
somewhat regular order; that between Mars and Jupiter, a 
wide gap destroys the symmetry otherwise apparent. Kepler 
suggested that a new planet might be found in this space. 

425. The series of Titius. — Titius of Wittenberg 
sought for a simple series of numbers, which should repre- 
sent the relative distances of the planets from the sun. 
After many trials, he took the series, 

o, 3, 6, 12, 24, 48, 96, etc., 

in which each term after the second is twice the preceding 
term; adding 4 to each, he found numbers which indicate 
very nearly the relative distances, as shown in the following 
table, as the planets are now known. 

At the time when this series was observed, the Minor 
Planets, Uranus, and Neptune were not known.- 

When Herschel discovered , the planet Uranus, its distance 
was found to correspond with its number in the series, but a 
planet was still wanting whose distance should answer to the 
number 28. This vacancy has been found to be filled in a 

way not expected, as we shall describe. 

(226) 



THE MINOR PLANTS. 



227 







Actual Distances. 


Planets. 


Series of Titius. 






Millions. 


Earth = 10 


Mercury, 


+ 4 = 4 


36 


3-9 


Venus, 


3 + 4= 7 


6 7 


7 


1 


Earth, 


6 4/4- IO 


93 


10 




Mars, 


12 -\~. 4 = 16 


142 


15 


2 


Minor Planets, 


24 + 4 = 28 


250 


27 




Jupiter, 


48 + 4 = 52 


483 


52 




Saturn, 


96 -f- 4 = IO ° 


886 


95 




Uranus, 


192 -f- 4 — 196 


1780 


192 




Neptune, 


384 + 4 = 388 


2790 


300 





Following the series, Neptune's number should be 388; 
but his distance is 2790 and his number 300. Here the 
series fails. Instead of showing a law, it shows probably- 
only a remarkable coincidence. 

426. Discovery of Ceres. — In 1800 an association of 
astronomers determined to conduct a systematic search for a 
planet between Mars and Jupiter. January 1, 1801, Piazzi, 
at Palermo, saw a new star, which he at first thought was a 
comet; it proved to be a planet, and its orbit was found to 
occupy the place in question. To this planet he gave the 
name Ceres. But the symmetry of the system, which seemed 
to have been so fully established, was again disturbed during 
the next year by the discovery of another small planet at 
nearly the same distance; in a few years, two more were 
found. 

427. Farther discoveries. — In 1845 a fifth was dis- 
covered, and since then others have been added rapidly to 
the list, until at present (March, 1884,) about 220 have 
been found, and their orbits determined. They have been 
called Asteroids (star like), Planetoids (planet like), or Minor 
Plan lis. 

All move in elliptical orbits, in obedience to Kepler's 

three meat laws. 



228 



ELEMENTS OF ASTRONOMY. 



428. Their peculiar characteristics. — 

1, They can be seen only with the telescope, and even then 
are known to be planets only by their motion. The figure 
shows a portion of the sky as seen in the field of a telescope, 
crossed by the illuminated wires of the reticule (80); the 




Fig- 139- 



known stars are mapped on a corresponding chart, and the 
new planet is recognized by its motion across the field. 

Because so small, they are measured with the greatest 
difficulty. The largest is supposed to be not more than 300 
miles in diameter, with a surface not larger than that of 
some islands on the earth. Newcomb estimates that the 
combined volume of all which have been found would make 
a planet not exceeding 400 miles in diameter. 

2. Their orbits are very eccentric, and much inclined to 
the plane of the ecliptic. 

3. Their orbits are included in a broad ring, at a mean 
distance from the sun of 250 millions of miles. Most of 
them at perihelion come nearer the sun than the nearest at 
its aphelion. The orbits are so interlaced that, if they were 
material rings or hoops, one could not be lifted out of its 
place without taking all the others with it. 



THE MINOR PLANETS. 229 

429. Origin of the Minor Planets. — Dr. Olbers sug- 
gested that they are the fragments of a large planet shat- 
tered by an explosion. As the pieces of a shell, after 
bursting, retain the forward motion of the shell while they 
diverge from each other, so the fragments of an exploded 
planet must continue to revolve about the sun, their orbits 
being modified by the force of the explosion. 

To Olbers' theory it is objected that all the orbits which 
the several parts might assume would necessarily meet at the 
point in space where the explosion occurred, each fragment 
returning to that point at regular intervals. But no common 
point is found. In fact, the path of the nearest is never 
within 50 millions of miles of the orbit of the farthest. Yet 
such a point may have existed, and the attractions of these 
planets upon each other, and of the planets on either -side, 
may have so changed their orbits as to cause them to diverge, 
and to cease passing through this common point. 

430. The Nebular Theory (Chap. XXIII) supposes that 
each of the planets was formed originally by the gathering 
of matter collected by gravitation, that, while the matter in 
the case of Jupiter or Mars concentrated about one nucleus, 
that which formed the minor planets gathered about many 
centers, the several masses being formed about the same time, 
and at nearly the same distance from the sun ; that these 
numerous small bodies take the place of the one large body 
which might have been formed had all been compacted into 
one. Thus the symmetry of the system is preserved even in 
its variety. 

431. Names and Symbols. — The discoverers of minor 
planets assigned names of goddesses from the ancient 
mythologies, but the list has already grown too long to be 
easily remembered. It is deemed better to indicate each 
by a small circle, inclosing a number in the order of dis- 
covery; thus, Ceres is 0; Maximiliana, or Cybele, @; 
Feronia, ©• There is, perhaps, no limit to the number 



230 ELEMENTS OF ASTRONOMY. 

which may yet be found, except that many may be too small 
to be picked up by even the best telescopes. Meanwhile the 
number now known is so great that it is difficult to follow 
their motions. It has been suggested that most of those 
which have been caught may be turned loose again with no 
loss to the science of astronomy. 



432. RECAPITULATION. 

Search was made at the beginning of this century for a planet 
between Mars and Jupiter, indicated by the law of Titius. 

Instead of one, four were soon found; since 1845, about 200 have 
been discovered ; all are small, visible only by the telescope. 

Their orbits are eccentric, interlaced, and make large angles with the 
plane of the ecliptic. 

They are not believed to be fragments of a larger planet. 



CHAPTER XVIII. 

THE OUTER GROUP.— JUPITER. 

SIGN %, FROM THE INITIAL OF ZEUS, THE GREEK NAME 
OF JUPITER. 

433. Appearance. — Jupiter is known by his clear, steady 
light, surpassing in splendor the brightest stars in the sky. 
In the telescope he shows a beautiful orb, crossed by light 




Fig. 140. 



and dark bands, and accompanied by four lesser bodies, or 
moons. Galileo's discovery of the moons of Jupiter, in 
1610, was one of the first fruits of the telescope, and was 
of great value in establishing the truth of the Copernican 
system. At opposition they may be seen even with a good 
opera-glass. 

Jupiter will be in opposition February 20, 1885; March 



20, 1886; April 22, 1887; May 25, 1888; about 



dai 1 



later each year than in the year preceding. 

434. The belts. -When examined with a telescope o\ 
moderate power, the disc seems tobc crossed by broad grayish 



(aji) 



232 



ELEMENTS OF ASTRONOMY. 



belts, one on either side of the equator, while between them 
a brighter space, often distinctly rose-colored, marks the 
equatorial regions. Under higher magnification these belts 
resolve themselves into streaks and cloud-like masses of very 




Fig. 141 



varied forms, so constantly changing that the views of two 
successive nights are seldom alike. Amid these belts, spots 
appear, sometimes bright, sometimes dark. These move, 
but with some degree of irregularity, leading us to think that 
their motion is partly their own, partly that of the planet. 
In 1834, Airy followed the same spot for about six months, 
and, from its motions, determined the planet's rotation in 
9 h. 55 m. 21.3 sec. Other observers differ; and still others 
find that the spots near the equator have a slower motion 
than those farther away. 



JUPITER. 233 

435. Resemblances to the sun. — 1. The central parts 
of the disc are brighter than the margin. A satellite, making 
its transit before the disc, appears bright against a dark back- 
ground, when near the margin, but dark against a brighter 
background when near the center. The center is two or 
three times as bright as the limb. 

2. The light of Jupiter is thought to be brighter than it 
would be if it simply reflected light from the sun. In other 
words, this planet is suspected of shining partly by its own 
light. 

3. The rapid changes of its belts indicate a great activity, 
which would suggest great heat; greater than that which 
could be received from the sun at that distance. 

The careful study which has been given to this body with 
the help of modern instruments, leads to the belief that it 
has not yet reached the condition which has a cold and 
stable surface, like that of the earth, but that it is now at a 
high temperature, perhaps liquid, possibly gaseous, but cov- 
ered with dense clouds, which may be more or less self- 
luminous, as they rise from the hot interior. 

436. Dimensions and shape. — The mean diameter is 
nearly n times that of the earth (284); 85,700 miles. 

If the spheroidal form of the earth is due to its rotation, 
Jupiter should be flattened still more, because of the more 
rapid motion at its equator, caused both by greater size and 
by quicker rotation. It is possible to compute, from the 
laws of gravity and of motion, what this flattening should 
be, and observation shows that the theoretical results corre- 
spond with actual dimensions. The polar diameter is short- 
ened about one seventeenth. 

437. Moons. — The four moons are named in their order 
from the planet : lo, Europa, Ganymede, Callisto. In order 

of size they are, third, fourth, first, second; Ganymede is 
3700 miles in diameter, -a little smaller than Mars; Europa, 
the smallest, 2200,— a little larger than our moon. In the 



234 



ELEMENTS OF ASTRONOMY. 



Jovian sky, the disc of the first appears about as broad as 
our moon appears to us; the others are less. They revolve 
about Jupiter in elliptical orbits, in conformity with Kepler's 
laws. 



Name. 


Mean Distance. 


Period of 
Revolution. 


Diameter. 

Miles. 


Planet's Dia. 


Miles. 


Io, 

Europa, 
Ganymede, 
Callisto, 


6.05 
9.62 

15-35 
26.99 


259,000 

412,000 

658,000 

1,156,000 


1.77 days. 
3-55 
7-i5 
16.69 


2,500 
2,200 
3,700 
3,200 



438. Their eclipses. — Their orbits are inclined to the 
orbit of Jupiter but slightly, while Jupiter's orbit makes an 
angle of less than 2 with the plane of the ecliptic. Hence, 
each moon at each revolution is likely to pass into the 
shadow of the planet, and be eclipsed ; to pass behind the 
planet, and be occulted; or to pass between us and the planet, 
making a transit. It may also pass between the planet and 
the sun, causing at Jupiter a solar eclipse, and showing to 
us a black shadow crossing the disc. In Fig. 142 the first 
moon is eclipsed; the second makes a transit as seen from 
the earth, while its shadow makes an eclipse of the sun at a 
place on the planet; the third is in occultation, and is not 
visible from the earth. Reference has already been made 
to these eclipses as valuable for determining terrestrial 
longitude (113). 

439. Orbit of Jupiter. — A complete revolution is made 
in about 12 years (4332.6 days). From this (274), his mean 
distance is found to be 483 millions of miles. The eccen- 
tricity is about 23 millions of miles, or 0.0483. The plane 
of the orbit makes, with that of the ecliptic, an angle of 
little more than i° (i° 18' 41"). The planet moves at a rate 
of about 8 miles a second. 



SA TURN. 



235 




Fig. 142. 



SA TURN. 



SIGN J? , A RUDE SCYTHE, OR SICKLE. 



440. Appearance. — Saturn shines with a steady silvery 
light, like a star of the fust magnitude, but without twinkling. 
In the telescope it presents a most magnificent display, re- 
vealing a system of satellites and a splendor o\ rings which 

surpass the glory of the entire solar system as known to 



236 ELEMENTS OF ASTRONOMY. 

Ptolemy. The times most favorable for observation will be 
about December 24, 1885; January 6, 1886; January 19, 
1887, etc.; each year about 13 days later than on the year 
preceding. 

The disc, like that of Jupiter, is crossed by streaks or 
belts, which are less distinctly seen because of greater dis- 
tance. In 1876, a notable white spot appeared near the 
equator, and, from its movements, Hall found the time of 
the planet's rotation to be 10 h. 14 m., a time a little less 
than that previously given by W. Herschel. 

The inclination of the axis to the plane of its orbit has 
been given at about 63 °. As might be expected from the 
rate of rotation, the sphere is flattened; its polar diameter 
is shortened about one tenth (Bessel), or one ninth (Hind). 

The mean diameter of the planet is about 70,000 miles. 



THE RINGS OF SATURN. 

441. Galileo's discovery. — To Galileo, in 1610, the. 
planet showed an oval disc, or a central body with two 
semilunar wings. Hence, he supposed it to be a triple 
body, a large planet with two constant attendants. Two 
years later, he again examined the planet, but the attendants 
had vanished. This fact, now well understood, gave him 
much anxiety, and led him to fear that he might have been 
deceived in other discoveries. "Can it be possible," said 
he, "that some demon has mocked me?" 

442. Huyghens' discoveries. — In 1655, Huyghens 
saw, in a more powerful telescope, that Saturn is surrounded 
by a broad, thin ring, nearly parallel to the planet's equator, 
and inclined to the ecliptic about 2 8°. The plane of the 
ring, like the axis of the earth (217), is always parallel to 
itself; in certain relative positions of Saturn and the earth, 
one side of the ring is visible; in others, the opposite side; 
in going from one to the other, the earth passes a point where 



THE RINGS OF SATURN. 



237 



only the edge of the ring can be seen, invisible in telescopes 
of lower power, and in larger instruments appearing as an 
extremely fine, bright line. It was this vanishing of the 
ring which puzzled Galileo. 



18S5 


.^Mg 


tafc-f'; 


iW8 




y r - 

ip 1 

' : '!;::.v- ;"•_.. 


38 /X 

: 


r 






....-■:■ . ' . ■ ■'• . . ■ ■■• 


V 1869 



Fig. 143- 



In 1665, two English observers, named Ball, perceived 
the dark streak which separates the ring into two principal 
parts. It is said that stars have been seen through this dark 
streak, showing that the space is devoid of solid matter. 
Other streaks have been seen at various times, but none 
remain permanently visible; were all verified, there would be 
at least five concentric bright rings. 

443. Bond's discovery. — In 1850, Bond saw. within 
the bright rings before known, a ring o( faint gray light, so 
transparent that the planet is visible through it. At first, it 
was thought that some important change had occurred, but 
records of former observations show that it had been seen 



2 3 8 



ELEMENTS OF ASTRONOMY. 



before, and mistaken for a belt on the surface of the planet ; 
on the other hand, it appears that when discovered it was an 
object not easily observed, and that now it may be seen in a 
telescope of moderate power. 

Mr. Bond first recognized its true character; very soon 
Otto Struve and Dawes perceived and measured a dark 
line in this ring. 




Fig. 144. 



444. Dimensions of the rings. — The equatorial diam- 
eter of Saturn is about 74,000 miles. The dimensions of 
the rings, giving the mean results of Struve and De la Rue, 
are nearly as follows, measured from the planet's center: 



Equatorial radius of planet, miles, 




37,000 


Space to dark ring, 


8,000 


45,000 


Space to bright ring, 


18,000 


55>°°° 


Breadth of inner bright ring, 


16,500 


71, 5°° 


Space between rings, 


1,500 


73,000 


Breadth of outer ring, 


10,000 


83,000 


Diameter of outer ring, 




166,000 



The thickness is variously estimated at from 40 to 250 
miles. When the edge only is visible, it shows in the tele- 
scope a bright line, so delicate that the fine spider-line in the 



SATURN. 239 

focus of the instrument seems a cable by comparison. At 
the same time the satellites which revolve in nearly the same 
plane are seen moving along this line of light, ' ' like pearls 
strung on a silver thread." 

The rings revolve in their own plane about the center of 
the planet in 10 h. 32 m. 

445. What are the rings? — Their brightness and the 
shadows which they cast upon the planet indicate that they 
consist of solid, or at least of opaque, material. The dark 
lines which streak them, showing either constant or only 
occasional separation into distinct bands, indicate that the 
solid particles do not cohere. Pierce demonstrated that they 
are not solid, and Clerk Maxwell that they are not liquid; 
the appearance of the dark ring and an apparent increase in 
breadth of the whole system since the days of Huyghens, 
of some 29 miles a year, corroborate this opinion. 

Our moon is kept in its place by the combined forces of 
gravitation and revolution in its orbit. A second moon fol- 
lowing in its path would be supported in the same way. We 
may conceive of a procession of moons following each other 
in immediate succession, each moon, and, in fact, each par- 
ticle in each moon, whether adhering to another particle or 
not, sustained independently of all the other members of the 
procession. So each particle in the rings of Saturn is a 
satellite revolving about its primary in obedience to the laws 
of planetary motion. 

To complete the hypothesis, it is supposed that the dark 
inner ring consists of comparatively few particles which have 
been removed from the denser crowd oi' the bright rings by 
the irregular attraction of the satellites in their revolutions; 
while the general increase in width, if a tact, is explained in 
the same way. 

446. Experiment.- Invert a large glass receiver, with 
swelled sides, such as is used with an air-pump, and suspend 



240 



ELEMENTS OF ASTRONOMY. 



it by a triple cord to a hook in the ceiling. Pour a few- 
ounces of mercury into the receiver, and twist up the cord; 
when the glass is set free, the untwist- 
ing cord causes rapid rotation, and the 
mercury, obeying the tangential force, 
flashes into the swell and revolves there 
in a continuous ring. A few shot, or 
marbles, illustrate a ring of non-coherent 
solid particles. 

A glass jar upon a whirling-table 
shows the same results. 

447. Satellites. — Besides the sys- 
tem of rings, Saturn has eight moons. 
Their names in order, beginning with 
the nearest, are Mimas, Enceladus, 
Tethys, Dione, Rhea, Titan, Hyperion, 
Japetus. Titan is the largest, with a 
diameter of 3,000 miles: the diameters 
of the others are approximately as given 
in the table. The orbit of the outer is 

Fig. 145. 

inclined 12 14' to the plane of the 
rings; the others nearly coincide with it. 




Name. 


Mean Distance. 


Period. 
Days. 


Diameter. 
Miles. 


Rad. of h- 


Miles. 


Mimas, 


3-4 


115,000 


O.94 


1,000 


Enceladus, 


4-3 


150,000 


1-37 


? 


Tethys, 


5-3 


185,000 


1.88 


500 


Dione, 


6.8 


238,000 


2-73 


500 


Rhea, 


9.6 


332,000 


4-5i 


1,200 


Titan, 


22.2 


770,000 


15-94 


3,200 


Hyperion, 


26.8 


988,000 


21.29 


? 


japetus, 


64.4 


2,254,000 


79-33 


I,8oo 



448. Orbit. — A complete revolution of Saturn occupies 
about 30 years (10,759.2 days). The mean radius vector 



URANUS. 241 

is 886 millions of miles; the eccentricity being about 50 
millions, or 0.056. The angle with the ecliptic is about 
2}i° (2 29' 39"). The rate of motion in its orbit averages 
rather less than 6 miles a second. 



URANUS. 

SIGN #, THE INITIAL OF HERSCHEL, WITH A GLOBE 
SUSPENDED FROM THE CROSS-BAR. 

449. Discovery. — In 1781, Sir William Herschel, while 
examining the small stars within the sweep of his telescope, 
saw one which showed a well-defined disc; continued obser- 
vation detected a change of place. The new body was 
thought to be a comet. Farther observation and the compu- 
tation of its orbit, proved it to be a great planet, before 
unknown. Herschel proposed to name the stranger the 
Georgium Sidus, in honor of the reigning king of England. 
La Place proposed to call it Herschel, for its discoverer. It 
finally received the name of Uranus, who, in the ancient 
mythology, was the father of Saturn. 

By tracing back the path of the planet, records were found 
of more than twenty observations, made during the ninety 
years previous to the discovery of Herschel, but the observers 
had thought it a fixed star. Lemonnier had observed it no 
less than twelve times, and missed the honor of its discovery 
by his want of method in recording his observations. 

450. Appearance. — When nearest the earth Uranus 
appears like a star of the sixth magnitude, and may be seen 

without a telescope. It will he in opposition about March 
23, [885, and each year ahout 4'.. days later than in the 
year preceding. The disc is too small to be measured easily. 
The diameter is believed to be about 32,000 miles. Miidler 
found a flattening of , 1 ; but other observers are unable to 

Ast— 16. 



242 



ELEMENTS OF ASTRONOMY. 



verify it. The axis may lie near the plane of the ecliptic; 
the body would then seem to be circular while the pole is 
turned toward the earth, and would show oblateness only 




Fig. 146. 

when both ends of the axis are visible. The position of the 
orbits of the satellites lends probability to this suggestion. 

The flattened shape indicates rotation, but no time of rota- 
tion has been determined. 



451. 
added 



Satellites. — Herschel reported six and Lassell 
two others. Only two of Herschel's have been 



verified, and it is now believed that but four exist. They 
are named Ariel, Umbriel, Titania, and Oberon. Unlike 
any planets or satellites before known, they have a retrograde 
motion almost at right angles to the plane of the planet's 
path. Instead of calling the motion retrograde at an angle 
of 79 , it may be considered direct at an angle of 101 . 



Name. 


Mean Distance. 


Period. 
Days. 


Diameter. 

Miles. 


Rad. of fp. 


Miles. 


Ariel, 
Umbriel, 
Titania, 
Oberon, 


7-44 
IO-37 
17.OI 

22.75 


119,000 
166,000 
272,000 
364,000 


2.52 

4.I4 

8.71 

13.46 


? 
? 
? 
? 



NEPTUNE. 243 

452. Orbit. — The sidereal revolution occupies about 84 
years (30,686.8 days). Its mean distance is about 1780 
millions of miles, the eccentricity being .046. The angle 
of the orbit with the plane of the ecliptic is about ^ of a 
degree (46' 21"). The rate of motion is about 4.2 miles a 
second. 



NEPTUNE. 
SIGN W, A TRIDENT. 

453. Disturbing influences of planets upon each 
other. — A planet influenced by no other attraction than that 
of the sun, would describe an exact ellipse with one focus at 
the sun. But no planet is so situated; in every case the path 
is modified in some degree by the attractions of other bodies 
in the system. As the places and masses of the bodies are 
known, their influences on each other are calculated; and 
from these data, tables have been computed, predicting the 
places of each for many years. Bouvard constructed such 
tables for Uranus, but the planet did not answer the predic- 
tions. Its motions led astronomers to look beyond its orbit 
for some large unknown body, whose attraction would 
account for the irregularities observed. 

454. Discovery of Neptune. — The solution of the 
problem, known to be very difficult, 'and by many deemed 
impossible, was undertaken in 1843 Dv Adams of Cambridge, 
England, and not long after by Leverrier of Paris, each being 
ignorant of the purpose of the other. The results thus inde- 
pendently obtained agreed within i°. Adams sent his to the 
Astronomer Royal at Greenwich, in October. 1845, nul 
observations were not made before July of the next year, and 
did not then effect a discovery. On the 31st o( August, 
[846, Leverrier published his results ami sent them to the 
observatories in Europe. On the 23d o\ September, the 



244 ELEMENTS OE ASTRONOMY. 

very day on which the information was received, Galle, at 
Berlin, having also received a new and accurate map of the 
quarter of the heavens indicated, turned his telescope thither, 
and found the predicted planet within 52' of the place which 
Leverrier had assigned. The predicted diameter was 3.3", 
the observed 3". 

455. The discovery perfected. — The new planet was 
soon found to be following an orbit somewhat different from 
that predicted by Adams and Leverrier. An exact deter- 
mination of its path from observation required data extend- 
ing over many years. Search was made by European 
astronomers to see if it, like Uranus, had not been at some 
time mistaken for a fixed star, but without success. 

Mr. Sears C. Walker, of Philadelphia, computed, from the 
few observations taken, a new orbit, and by tracing this 
back, found that the planet had been twice observed in 1795, 
by Lalande, who recorded it as a fixed star. Lalande, being 
afterward unable to find the star in the same place, had 
marked his previous observations as doubtful, and Walker 
found its place vacant. But the new orbit accorded with the 
observations of Lalande, and of 1846, while the motion of 
the planet along this path accounted for all the perturbations 
of Uranus during that period. 

Thus the orbit and the observations mutually verify each 
other, while to an American belongs the honor of perfecting 
the discovery of this remotest known member of our solar 
system, — the most remarkable triumph of mathematical 
astronomy. 

456. The planet. — In the telescope, Neptune has the 
aspect of a star of the eighth magnitude. Its diameter is 
about 35,000 miles. No spot, or flattening of shape, has 
been observed; hence, nothing is known of its rotation. 
Its time of revolution is about 165 years (60,126.7 days). 
The orbit has a mean radius of 2790 millions of miles, with 
an eccentricity of 0.0089, an d is inclined to the ecliptic 



ASTRONOMICAL APPARATUS. 245 

about i^° (i° 46' 59"). Its rate of motion is about 3^ 
miles a second. 

As before remarked (425), Neptune's distance from the 
sun does not conform to the Series of Titius, which by this 
fact is recognized only as a notable coincidence. 

457. Satellite. — Only one moon is known, although the 
existence of another has been suspected. The known sat- 
ellite revolves in 5 d. 21 h., at a distance of 210,000 miles. 
Its motion is retrograde, in an orbit nearly circular, inclined 
34 53' to the orbit of the planet. From this moon, the mass 
of the primary is found (293), and from the mass its density, 
which is little more than that of water. 



ASTRONOMICAL APPARATUS. 

458. Diagrams and Orreries. — The inadequacy of 
diagrams, or of machines, to represent the distances and 
motions of the planets is strikingly shown in the following 
quotation from Herschel's Outlines of Astronomy : 

''Choose any well leveled field or bowling-green. On it 
place a globe, two feet in diameter; this will represent the 
sun; Mercury will be represented by a grain of mustard- 
seed, on the circumference of a circle 164 feet in diameter, 
for its orbit; Venus, a pea, on a circle 284 feet in diameter; 
the Earth, also a pea, on a circle of 430 feet; Mars, a rather 
large pin's head, on a circle of 654 feet; the Minor Planets, 
grains of sand, on circles of from 1000 to 1200 feet ; Jupiter, 
a moderate sized orange, on a circle nearly half a mile across; 
Saturn, a small orange, on a circle four fifths o( a mile; 
Uranus, a full sized cherry, upon the circumference o\ more 
than a mile and a half; and Neptune, a good sized plum, on 
a circle about two miles ami a half in diameter. 

"As to getting correct notions oi this subject in drawing 

circles on paper, or, still worse, from those very childish toys, 



246 ELEMENTS OF ASTRONOMY. 

called orreries, it is out of the question. To imitate the mo- 
tions of the planets, in the above-mentioned orbits, Mercury 
must describe its own diameter in 41 seconds; Venus, in 4 
m. 14 s.; the Earth, in 7 m. ; Mars, in 4 m. 48 s. ; Jupiter, 
in 2 h. 56 m. ; Saturn, in 3 h. 13 m. * Uranus, in 2 h. 16 m. ; 
and Neptune, in 3 h. 30 m." 



459. RECAPITULATION OF OUTER GROUP. 

The four planets, Jupiter, Saturn, Uranus, and Neptune, form what 
may be called the outer group of planets. In certain respects they are 
like each other, and unlike the planets of the inner group. 

In size, Uranus and Neptune have about 4, Saturn, 10, and Jupiter, 
11, times the diameter of the earth. 

The time of rotation of Jupiter and Saturn, about 10 hours, is notable 
for its shortness, especially when size is considered, and when com- 
pared with the 24 hours of the inner planets. 

In density, each is not greatly different from water; Jupiter and 
Uranus are each about one fourth more, while Saturn is about as 
much less. 

All are attended by satellites ; those of Uranus and Neptune are 
notable for moving from east to west, unlike any other bodies in the 
system. 

Jupiter. Saturn. Uranus. Neptune. 

Size, 86,000 70,000 32,000 35,ooo 



Solar day, 


9 h 


•55 m. 


10 


h. 14m. 






Density, 




1.4 




0-75 


1.28 


r.15 


Satellites, 




4 




8 


4 


1 


Distance from sun ^ 
In millions of m. t 




483 




886 


1780 


2790 


Velocity in orbit, m. 




8.06 




5-95 


4.20 


3-36 



CHAPTER XIX. 



COMETS. 



460. The name. — The ancients gave the name comet* 
to those brilliant objects which appear, suddenly and for a 
brief period, in the sky, and are usually attended by long 
flaming trains. The telescope shows that they consist 
mainly of misty, nebulous substance, and it reveals many 
similar bodies not attended by luminous trains. However 
irregular their apparent motions, they move in well-known 
curves, and always about the sun as their common center 
of attraction. 

461. Numbers. — The Chinese have recorded the advent 
of comets since about 600 years before the Christian Era. 
Including those records, the lists of comets for the last 2500 
years mention between 700 and 800. But, in earl}' ages, 
only the most remarkable were noted ; while of the mam- 
seen during the last two centuries, most have been visible 
only with the telescope. Doubtless a like proportion passed 
previously without record. 

Very many comets were not formerly seen, and are not 
now, because they appear above our horizon only in the day 
time; a large comet was once revealed by an eclipse o\ the 
sun. The number, therefore, of comets which have passed 
the earth during the historic period must be several thou 
sand. If this number be increased by those which had 



Ko///)r//(,\ kometeS) wearing long hair. 

(147) 



248 ELEMENTS OF ASTRONOMY. 

previously visited our sky, and by the multitudes now on the 
way to blaze in our heavens during the centuries to come; 
and be farther augmented by the myriads more which doubt- 
less enter our system, but pass the sun too far away to be 
seen at the earth; we may readily conclude, with Arago, that 
the comets belonging to the solar system are numbered by 
millions, and with Kepler, that they are countless, "as the 
fishes in the sea." 

PARTS OF A COMET. 

462. The bright point near the center of the principal 
mass of a comet is called the nucleus ; the light haze about 
the nuclues is the coma; the two together form the head. 
The luminous trail is the tail. Often the tail is absent, 




Fig. 147. — Comet without tail. Comet without nucleus. 

especially from the smaller comets, and occasionally no 
nucleus is found; the comet being merely a globular mass 
of coma. The stream of light which forms the tail, appears 
to issue from the head toward the sun, and then, as if blown 
away by some repulsion in that body, it is folded back about 
the nucleus, and swept far out into space. 

463. Comets are material. — This is evident, since they 
obey the laws of gravitation. They move about the sun in 



PARTS OF A COMET. 249 

regular orbits; their returns have been successfully predicted; 
and they are influenced by the attraction of planets in whose 
vicinity they pass. 

But this material substance is exceedingly rare. Small 
stars have been distinctly seen through the densest part of a 
comet, where its diameter was 50,000 to 100,000 miles; the 
same stars would be completely obscured by the rarest fog, 
or the lightest cloud. Evidence of more value to the astron- 
omer is the fact that large comets have passed near planets 
and satellites without causing the least perceptible disturb- 
ance in the motions of those masses. 

The spectroscope indicates that the nucleus of a comet is 
self-luminous at a high temperature ; and that the substance 
about the nucleus contains a compound of hydrogen and 
carbon. 

The spectroscope, and in a measure the polariscope indi- 
cate that the light from comets is also in some degree re- 
flected from the sun. 

464. Apparent dimensions. — The comets of 1618 and 
1861 covered more than ioo° in the sky; the tail might have 
passed the zenith, while the head was still below the horizon. 
The length of the comet of 1680 was variously stated at from 
70 to 90 ; that of the comet of 1843 was estimated at about 



IS 



65 °. The light of the tail often fades so gradually that it 
very difficult to tell where it ends. This wonderful append- 
age, that streams across the sky like a flaming sword, has 
made the appearance of a great comet an occasion ot terror 
during most ages of the world. 

465. Variations.- Some o( the brightest comets have 

had short and feeble tails, and some great comets have had 
none. Cassini mentions two whose discs were as round and 
as distinct as Jupiter. 

A small comet in [823 had two distinct tails. the brighter 
being turned from the sun, while a smaller one nearly 
Opposite was turned toward the suu. 



25° 



ELEMENTS OF ASTRONOMY. 



The tail of the comet of 1744 was divided into many 
branches, as if there were several distinct tails. 

466. Actual dimensions. — The apparent size of a 
comet does not always indicate its actual length; a long 
tail would appear short to an observer in certain positions. 




Fig. 148. — Comet of 1744. 



The actual diameter of the nucleus, when any is seen, is 
estimated at from 25 to 800 miles, rarely more than 500. 
The coma has sometimes a diameter of 200,000 to 350,000 
miles; that of the comet of 181 1 was 1,125,000 miles. The 
tail of the same comet was more than 100 millions of miles 
long; that of the comet of 1680, when largest, was nearly 
125 millions of miles in length, — one third longer than the 
distance from the earth to the sun. 



THE TAIL. 251 



THE TAIL. 

467. The development of the tail. — When a comet 
is first seen, it has usually little or no tail; as it approaches 
the sun, the coma expands, and the tail grows longer and 
brighter. While passing the sun, it sometimes expands with 
a rapidity almost inconceivable. The tail of the comet of 
1858 grew two millions of miles daily; that of 181 1, nine 
millions; and that of 1843 expanded seventy millions of miles 
in two days. After the comet has passed the sun, the tail 
diminishes again, and has often nearly vanished before the 
head disappears. 

468. The cause of the tail. — Its position, always turned 
from the sun, its increase when approaching that body, its 
decrease when retiring, all indicate that it is produced by 
some unknown repulsive power in the sun, unlike gravita- 
tion, and opposed to it. The supposition that the comet 
carries its tail along with it involves consequences that could 
not exist. Stretching so far away as the dimensions some- 
times found, if the tail were swinging around like the spoke 
of a wheel, the outer parts must be moving at such a rate as 
would overcome all radial force, and send the separated frag- 
ments far out into space. Newcomb suggests that the tail 
is a stream of vapor emanating from the comet like smoke 
from a chimney, constantly floating away, and constantly 
renewed. 

469. The curvature of the tail gives a hint of the way 
in which it is formed, though not of the force. Suppose the 
nucleus moves along the curve ABC, about the sun. When 
at A, the unknown power in the sun drives a particle oi 
matter from the coma, with a force which can carry it to 
/), while the nucleus moves to C; the particle, obedient to 
this repulsion, and to the forward motion which it had on 
AC, is found at E, as far forward oi the line AD as the 



252 



ELEMENTS OF ASTRONOMY. 



distance through which the head has moved; it is not in 
the line SCL, passing through the sun and the nucleus. 

While the head is at B, half way from A to C, another 
particle is repelled, which in like manner may be traced to 




Fig. 149. 

the point H. This point is also behind the line SZ, but 
not half as much as the point E, because BG, the line of 
the second repulsive action, is not parallel to AD, the line 
of the first. Similarly, all the particles in the tail find their 
places, and the tail is always convex toward the direction in 
which the comet moves. 

470. The tail hollow. — It is usually remarked that the 
edges of the tail are brighter than the portion between; there 




Fig. 150. 



seem to be two streams of light connected by a fainter web. 
This indicates that the tail is hollow, — a constantly expand- 
ing tube. Its cross section is a ring, either circular or oval, 
as in the figure; more luminous matter lies in the lines of 
AB and AD than in AC. 



THE HEAD. 253 



THE HEAD. 

471. Variations of the head. — When the comet comes 
near the sun, both nucleus and coma often diminish, to in- 
crease again as the body recedes. It has been suggested 
that the intense heat may expand the substance of the comet 
into transparent, invisible vapor; when the heat diminishes, this 
vapor, like steam, may become visible again in cooling. As 
the diminution of the head occurs at the same time as the 
expansion of the tail, one fact may explain the other; the 
substance being re-pelled to form the tail. 

472. Is the nucleus solid ? — Herschel saw a star of the 
twentieth magnitude, through the brightest part of a comet. 
Messier, while observing a comet, saw, after a time, a small 
star near, which he thought the comet had concealed, as he 
had not noticed it before, but he did not see either the begin- 
ning or the end of the occultation. 

The fact that comets show no phases, is important but not 
conclusive, as they may shine, in part at least, by their own 
light. Arago proved by the polariscope that a portion of the 
light is reflected from the sun. This may be the fact, and 
the comet be self-luminous also. 



THE ORBITS OF COMETS. 

473. The cone. — When a line, AB (Fig. 151), revolves 

about another line, CD, which it crosses obliquely at /", it 
produces two surfaces, each of which we ordinarily consider 
the surface of a cone; but as both surfaces arc generated at 
once by the revolution of one line, they arc deemed two 
parts or sheets of the same conical surface. 

CD is its axis. The line AB in any position, as ./'/>". is 
an element ol~ the cone. 



254 



ELEMENTS OF ASTRONOMY. 



474. The conic sections. — Through any point, P, in 
either sheet of the cone, pass a plane perpendicular to the 
axis; the intersection is a circle, PE, being its diameter. 

Keeping the point P fixed, turn the cutting plane, 
making it intersect the opposite element either above or 

below E, as at R ; the section is 
an ellipse, and PR is . its major 
axis. 

A circle is one variety of the 
ellipse (188). 

Turn the plane until it is par- 
allel to the opposite element of 
the cone; the section is now 
a parabola. Evidently the two 
branches of the parabola can 
never meet each other or the 
opposite element of the cone. It 
is an ellipse whose major axis, 
Px, is infinite. 

Turn the plane yet farther. It 
now cuts the opposite sheet of 
the cone; the section is a hyper- 
bola. Its branches can never 
meet, but may go on infinitely, 
becoming more and more nearly 
straight lines. 
These three curves, the ellipse, the parabola, and the 
hyperbola, with their possible varieties, are known as the 
conic sections. They have each at least one vertex, which 
answers to the point P ; a major axis, which passes through 
the vertex, and either meets, or is parallel to, the axis, CD, 
of the cone ; and at least one focus. 




475. The general law of celestial motion. — Newton 
demonstrated mathematically that a body must move in the 
curve of some one of the conic sections, if impelled by two 



THE ORBITS OF COMETS. 



255 



forces, one of which is a constant central force, as the 
attraction of gravitation; and the other, a tangential or im- 
pulsive force. This led him to believe that comets obey 
the same laws which govern planets. 

The great comet of 1680 furnished an opportunity for 
testing this deduction. From a large number of observa- 




Fig. 152. 



tions, Newton found that its path was the curve of a par- 
abola, or of an ellipse so eccentric, and with a major axis 
so long, as not to be distinguished from a parabola; that 
the sun was at the focus; and that the radius vector de- 
scribed equal areas in equal times. 

476. The elements of a cometary orbit. — The orbit 
lies in a plane which passes through the sun's center, and 
which may have any degree o\ obliquity to the ecliptic. 
The terms perihelion^ aphelion, ascending node, and descend- 
ing node have the same meaning as in the orbits of the 
planets. 



256 



ELEMENTS OF ASTRONOMY. 



Let .S be the sun; CERE', the ecliptic; and the inner 
curve, part of a cometary orbit. The curve EPE' is the 
apparent path of the comet on the sky, as seen from the 




VERNAL /E20" 

EQUINOX 

Fig. 153. 



sun, or as it would be traced on a celestial globe. To 
determine the orbit we find : 

1. The inclination, or the angle which the plane of 
orbit makes with the plane of the ecliptic. It is the angle 
PSR, or the angle which the two curves make at E, the as- 
cending node being always taken for the sake of uniformity. 

2. The position of the axis. — The axis passes through 
the focus, which is at S, and the vertex, which is at the 
perihelion. The apparent place of perihelion, on the sky, is 
at P. Suppose a circle drawn through P, perpendicular to 
the ecliptic, and meeting it at R; the longitude of R shows 
the position of the axis; it is called the longitude of the 
perihelion. 



COMETS OF LONG PERIOD. 257 

3. The position of the nodes. — The line of nodes, 
ESE' , passes through the sun; we have only to find the 
longitude of the ascending node; the other node is distant 
180 . 

4. The perihelion distance, which is the distance in 
miles of the perihelion from the center of the sun. 

5. The eccentricity. 

6. The motion is either direct, as in Fig. 153, or retro- 
grade. 

In the diagram, the angle of inclination is 40 ; the longi- 
tude of perihelion, 95 ; the longitude of the ascending 
node, 20 . 

477. How may -we know a comet on its re- 
appearance? — Not by its form. Since a comet changes 
so much during a single passage about the sun, we can 
hardly expect that the second series of changes should be 
like the first. It is very improbable that two comets would 
follow each other in the same orbit. If, then, the orbit of 
a comet has elements which agree closely with those of any 
other on record, we conclude that the two may be two 
appearances of the same body, especially if the orbit is 
elliptical. 

COMETS OF LONG PERIOD. 

478. Halley's comet. — The celebrated astronomer, 
Halley, having computed the elements of the great comet 
of 1682, found that it moved in an elliptical orbit very like 
those of the comets of 1607 and 1531, whose orbits he also 
computed from observations on record. He interred that 
the three comets were identical, and predicted a return 
about 1759. 

As the time approached, great interest was aroused among 
astronomers, and much pains was taken to investigate the 

Ast.— 17. 



258 ELEMENTS OF ASTRONOMY. 

effect of the attractions of the planets near which the comet 
would pass. The mathematical methods known to Halley 
could not have solved this problem. With improved 
methods, Clairaut found that the comet would be delayed 
by both Saturn and Jupiter, and that it would pass the peri- 
helion within a month of the middle of April, 1759. The 
passage occurred March 12th. 




Fig. 154.— Halley's Comet, Oct. 22, 1835. 

Several persons calculated its next return; the two results 
deemed most reliable fixed the day of perihelion for the nth 
and for the 26th of November, 1835. The passage was 
made on the 16th. Its next appearance is expected about 
1911. 

From the records of comets, it appears that seven ap- 
pearances of this comet have been noted, while five other 
dates correspond so nearly as to make it probable that they 
belong to the same list, extending back as far as n years 
b. c. The average period is 76 years 2 months. The orbit 
extends 600 millions of miles beyond that of Neptune. The 
motion is retrograde. 

The comet of 181 2, called Pons's Comet, returned in 
January, 1884, after a period of about 72 years, very nearly 
as predicted. 



COMETS OF SHORT PERIOD. 



259 



479. Other comets of long period. — No other comets 
of long period have verified predictions of their return. Of 
about 200 computed orbits, about 50 are thought to be 
ellipses; seven are hyperbolas, and the rest are parabolas. 
Most of the computed periods are long, reaching to hun- 
dreds, and even thousands, of years. A few are given for 
illustration : 



Comet of 


Years. 


Comet of 


Years. 


i843> 


376 


1680, 


8,813 


1846, 


4OI 


1780, 


75,838 


1811, 


3065 


1844, 


100,000 



COMETS OF SHORT PERIOD. 



480. Ten comets have appeared, whose calculated 
periods are less than 14 years, and that have returned to 
verify such calculations. They are all telescopic, and, but 
for their returns as predicted, are of little general interest. 
They have been named from those who have determined 
their orbits: 



Name. 



En eke 's 

Winnecke's 

Brorsen's 

Tempel's I. 

D'Arrest's 

Biela's 

Faye's 

Turtle's 

Tempel's 1 1. 

Swift's 



Last 
Return. 



l88l, 
1875, 
1879, 
1879, 
1883, 
1852, 
1880, 
1871, 
l88 3> 
1880, 



Nov. 
Mch. 
Mch. 

May 
Oet. 

Sept. 
Dee. 
Dee. 

Nov. 
Nov. 



Least 


Greatest 


Periodic 


Distance. 


Distance. 


Times. 


O.342 


4.IO 


3-304 


O.78 


5-5° 


5-^43 


O.62 


5.66 


5-561 


1.77 


4.S2 


6.00 


1. 17 


5-72 


6.39 


0.S6 


6.19 


6.62 


1.69 


5.92 


7.4I 


1.03 


10.51 


[3.78 


1-34 


4.00 


5.20 


1.07 


5.14 


5-50 



Next 
Return. 



1885, Mch. 

1886, June 

1554. Oct. 

1555. May 
1S00. Feb. 

iSSS. May 
1885, St T l - 
1SS0. Jan. 
1SS0. May 



481. Do comets meet a resisting medium? — The 
period of Encke's comet is gradually diminishing, losing one 



260 ELEMENTS OF ASTRONOMY. 

day in about ten revolutions. This indicates that some 
cause checks the forward or tangential force of this comet, 
leaving the radial force of the sun to draw it more swiftly 
about itself. Encke supposed that it is retarded by a re- 
sisting medium, or ether, which is densest near the sun. 

The same opinion was held concerning the period of 
Faye's comet, but continued observation has shown that 
the motion of this comet is not changed. Encke's theory 
of a resisting ether meets little favor. 

The resistance to Encke's comet may be explained by 
some cause other than a resisting ether. For example, 
the comet might meet a ring of meteoric matter, which 
could be a serious delay to it. 



REMARKABLE COMETS. 

482. A double comet. — Soon after Biela's, also called 
Gambart's, comet appeared in 1846, its head was seen to 




Fig- 155. 



become elongated or pear-shaped. In a few days two comets 
were seen moving side by side. The attendant, though at 
first smaller, gradually increased until it became brighter 



REMARKABLE COMETS. 26 1 

than the old; afterward it diminished until it was not easily 
seen. Each part had its own nucleus, coma, and tail; one 
observer saw a stream of light, which seemed, like a bridge, 
to span the abyss between them. On the return of the 
comet in 1852, it was still divided, and the parts had be- 
come more widely separated. Since then it has not been 
seen, and it is now supposed to be a lost comet, perhaps 
wholly disintegrated. 

483. Danger of collision. — The path of this comet lies 
so near the orbit of the earth that if the two bodies were to 
pass at the same instant they would collide, like trains at 
the crossing of two railways. In 1832, the comet passed 
this point about a month before the earth, but as the earth, 
though making her usual time, was then more than 45 
millions of miles away, there was no occasion for fear. 

Direct collision between a comet and a planet is very 
improbable. Arago computes the chance at one in about 
287 millions. The result of such a meeting can not be 
guessed until more is known of the nature of comets. 
Many think their substance so rare, and both it and the 
air so elastic, that the mass of the comet could not reach 
the earth. We have several times passed near the tail of 
a comet, and Hind supposed that in 1861 the earth passed 
quite through one, but no effect other than a peculiar 
phosphorescent mist was perceived. 

484. Lexell's comet is remarkable because its cubit 
has been twice changed by the force of Jupiter's attraction. 
It appeared in \*]*]o, and was found to describe an elliptical 
orbit in about 5^ years. Surprise was felt that a comet o\ 
some brilliancy, and having so short a period, had not been 
seen before. By tracing its motions, l.exell found that as 
it passed Jupiter, it had been turned aside from its old path 
into a new and shorter one; that its old period had been 
48 years, and its perihelion distance 300 millions oi miles; 
at that distance it could never be visible at the earth. 



262 



ELEMENTS OF ASTRONOMY. 



485. A second change. — When the comet approaxhed 
its new aphelion, which was within the orbit of Jupiter, it 
again found that planet in the neighborhood, and its path 
was a second time changed. The third orbit, though unlike 
either of the others, has elements which remove it from 
sight at the earth, where it will never again be seen, unless 
some adequate attraction shall change its course. Its new 
period is about 20 years, and its perihelion distance about 
300 millions of miles. 

In July, 1770, this comet passed within 1,400,000 miles 
of the earth, nearer than any other comet on record. Had 
its mass been equal to that of the earth, it is estimated 




Fig. 156. 



that this approach would have so changed the earth's orbit 
as to make the year 2 h. 48 m. longer than before. But 
the length of the year was not changed as much as two 
seconds; whence we infer that the mass must have been 



less than 



that of the earth. 



The changes in the orbit of this comet suggest that others 
may have been similarly disturbed. Comets that go away 
from the sun in parabolic orbits may wander out of the sphere 
of the sun's attraction and into that of some other center. 



REMARKABLE COMETS. 263 

In like manner, the wanderer may come from- some other 
system, and, passing near one of the planets, may be 
deflected into a new path which takes it about the sun in an 
ellipse of greater or less eccentricity, perhaps of short period 
and quick return. 

486. The great comet of 1843. — On the 28th of Feb- 
ruary, 1843, a comet appeared in the day-time, quite near 
the sun, the head and the beginning of the tail seeming like 
a dagger turned from the sun. In a few days it appeared 
after sunset, with a tail 65 ° in length. When its orbit was 
determined, it was found that its center had passed within 
80,000 miles of the sun's surface, and that the two bodies 
were distant not more than 32,000 miles; the heat to which 
it was subjected was more than 47,000 times as intense as 
the solar heat received at the surface of the earth, and more 
than 25 times that required to melt and vaporize agate and 
rock-crystal. Through this intensest fire, the comet whirled 
at a rate which increased its distance from the sun tenfold 
in one day. Its tail was 150 millions of miles long and 3 
millions broad. Its orbit is elliptic; some have deemed it 
identical with the comet of 1668, having a period of 175 
years. Hubbard computed its period at 530 years. 

487. Other recent comets. — Donati's comet appeared 
on the 2d of June, 1858; in October, it was a very beautiful 
object in the northern sky. The nucleus was not large; the 
tail was about 50 millions of miles in length, very brilliant, 
and of very graceful form. Its period is found by Hill to 
be 1950 years. 

The comet of 1861 was noted for its tail, which extended 
over more than ioo°. Its period is about 450 years. 

The comet of [862 formed frequent bright jets, like jets 
of steam, directed toward the sun. or to (he eastward, in a 
direction opposite to its motion. The material o( each jet 
seemed to drift away in the direction ol the tail. 



264 ELEMENTS OF ASTRONOMY. 

The comet of 1880 is remarkable for following very closely 
the orbit of the comet of 1843. The comet of 1881 is like- 
wise notable for following in the track of that of 1807. I n 
each case, however, the orbit is so definitely parabolic, that 
it is quite unlikely that the second body is a re-appearance 
of the first. 



488. RECAPITULATION. 

Comets are nebulous masses which move about the sun in very 
eccentric orbits. They are composed of very rare material, and usually 
show nucleus, coma, and tail. 

The tail is developed by some unknown repulsion in the sun as the 
comet approaches, and is probably lost. It is always curved from the 
direction of motion, and is tubular. The head dwiinishes as the comet 
comes near the sun. 

The path of a comet is always the curve of some one of the conic 
sections, and the motion conforms to the great laws of planetary motion. 

The elements of a comet's orbit are : Inclination ; longitude of peri- 
helion; longitude of ascending node; perihelion distance; eccentricity. 
Comets which have the same orbital elements are deemed identical. 

Halley's comet first returned in accordance with prediction. The 
periods of ten small comets are verified by returns. 

Biela's comet appeared in two portions, moving side by side, and is 
now believed to be lost. 

Lexell's comet had its orbit twice changed by the attraction of 
Jupiter. 



CHAPTER XX. 

METEORIC ASTRONOMY. 

489. Shooting-stars. — The bright objects which in a 
clear night suddenly glide along a portion of the sky, and as 
suddenly vanish, sometimes leaving a faint trail of light, are 
called shooting-stars. On a moonless night, a single observer 
may count an average of 8 an hour. As one person can see 
but about one fourth of the sky at once, it follows that about 
30 are visible in an hour, or more than 700 in a day, if none 
were obscured by sunlight. But the same observations may 
be made from more than 10,000 stations on the earth ; whence 
7 millions a day pass near enough to the earth to be seen. 
50 times as many may be seen with the telescope, as without, 
and this number increases with the power of the instrument. 
Professor Newton calls these bodies meteoroids. 

490. The November showers. — On the 12th of No- 
vember, 1833, a brilliant display of these meteors was 
observed throughout the eastern half of North America. 
Humboldt saw in South America a similar shower on the 
same month and day in 1799. Records were found of at 
least twelve other great November showers, at dates which 
answer very nearly to periods of 33 years. These and other 
facts caused the belief that these displays arc periodical, and 
that one would occur in 1866. In America, though more 
meteors were counted than are commonly seen, the shower 
bore little likeness to that of 1833; in Europe, the scene was 
more brilliant, and fully confirmed the predicted return. 



266 



ELEMENTS OF ASTRONOMY. 



In 1833, it was estimated that more than 200,000 meteors 
were visible at a single station. The lines on which they 
moved, when traced backward, were all found to diverge 
from a single point in the group of stars called Leo, the 

place in the sky to- 
ward which the earth 
was then moving in its 
orbit. 

The point from which 
numbers of shooting- 
stars seem to diverge, 
is called the radiant. 




Fig- 157. 



491. Height and 
velocity. — Observa- 
tions on the same me- 
teors from distant places 
show that they become 
visible at a distance of 
70 to 80 miles from the 
surface of the earth, 
and vanish at about 50 to 55 miles; that their average 
visible track is about 42 miles long, and the velocity is 
estimated at 26 to 34 miles per second. The November 
meteoroids move in a direction opposite to that of the earth. 
As the earth moves at the rate of 18 miles per second, the 
velocity of the meteoric body in the air must be more than 
44 miles per second. 

492. They do not originate in the air. — The radiant 
of the November meteoroids is in Leo, and remains un- 
changed for several hours, although the earth is rapidly turn- 
ing on its axis. Hence, they must come from some place 
beyond the atmosphere. Their speed being about 10 miles 
per second greater than that of the earth in its orbit, also 
shows that they move independently of the earth, and at 
planetary rates. 



METEORIC ASTRONOMY. 



267 



493. What are they ? — They are now believed to be 
planetary bodies that move about the sun in regular elliptical 
orbits, obeying the planetary laws. The November meteoroids 
are supposed to flow together in a broad and long stream or 
procession, in a very eccentric orbit, whose average period is 
33/^ years. The orbit crosses the earth's path, and the 
earth passes the crossing each 12th of November, finding 
always some meteors. On the years before, at, and after, 
the interval of ^ years, the earth meets the great stream of 
meteors, a stream so long as to be more than two years in 
passing any given point, and, therefore, met by the earth, on 
two or even three successive Novembers. 

The meteors are believed to be gaseous bodies, set on fire 
by friction with the air, through which they rush at such great 
speed; the products of combustion remain in the air. 

494. The orbit of the November meteoroids has been 
computed. Its perihelion is near the earth, and its aphelion 



pR 0BABUi 



ORBIT OF 




"OISEM8ER , METEORS. 



Fig. 158. 



beyond Uranus. The orbit coincides closely with that ot 
the comet of 1866, which is believed to be only a Large 
meteor, perhaps an aggregate of several, o( the November 

stream. 



268 



ELEMENTS OF ASTRONOMY. 



495. August meteoroids. — Many shooting-stars maybe 
seen about the 10th of August, and a few grand showers have 




Fig. 159 — Orbits of the August and November Meteor-showers. 
(Orbits of Comets III, 1862, and I, 1866.) 



occurred at that date. As the festival of St. Lawrence occurs 
on this day, the stars have been called, in Europe, St. Law- 
rence's tears, and the shower is known as the Laurentian 



BOLIDES. 269 

Shower. The radiant is in the graup Perseus. The ring, or 
stream, of these meteors is believed to have a period of 105 
years. Meteors constantly traverse every part of this orbit, 
and hence some are met every year, but at long intervals the 
crowd is quite dense. The comet of 1862 is referred to the 
August meteoric stream. 

Other dates bring more than the usual number of shooting- 
stars. The principal are, April 18-26; December 6-13; 
January 2, 3. 

496. Theories suggested. — In the discussion of me- 
teoric rings, these items have been suggested: 

That Biela's comet passed near and perhaps through the 
November stream, in December, 1845. The rushing stream 
may have divided the thin substance of the comet, as one 
vessel at sea cuts another in twain, in a collision. Since 
1852, this comet has not been seen, although its return has 
been carefully watched. Has it again met a stream of me- 
teors, to be quite broken up, material for future shooting- 
stars ? 

That the rings of Saturn may be meteoric streams, divided 
occasionally by the disturbing influence of the satellites. 

That the Minor Planets are a stream of meteors, the 
largest only being visible at the earth. 

That Encke's comet has been detained by meteoric 
streams. 

That the sun's heat is maintained by the constant falling 
of meteoric bodies upon its surface (326). 



BOLIDES. 

497. No sound is heard from ordinary shooting-stars, 
probably on account of their great distance. Other fiery 
masses sometimes pass over the earth, followed after a time 
by a rushing sound or the noise of an explosion. Sometimes 



2 7 o ELEMENTS OF AST R ONOMY. 

the explosion and the scattering fragments have been seen; 
at other times the sound seems to be caused by the swift 
flight of the mass through the air. 

The word meteor signifies any bright and transient object 
seen in the sky, including those just mentioned, shooting- 
stars, the aurora borealis, etc. Meteoric balls of fire are 
called bolides* About 800 have been recorded. 

498. Their motions. — In i860, a bolis passed over the 
country between Pittsburg and New Orleans. Soon after 
it vanished an explosion was heard like the noise of many 
cannon. It traversed a distance of 240 miles in 8 seconds, 
having a velocity, referred to the earth, of 30 miles a second; 
referred to the sun, of 24 miles per second. Such a velocity 
shows that the moving body can not come from any place 
near the earth ; the rate could not be acquired, even if it had 
fallen from the moon. The same conclusions follow, as in 
the case of the shooting-stars. 

Bolides frequently appear at the dates given as abounding 
in shooting-stars. They are probably similar, but larger, 
denser, and not so soon consumed in passing through the air. 



AEROLITES. 

499. In many authentic instances, masses of mineral 
substance have fallen from the sky; they are called aerolites, 
or "stones of the air." The explosion of a brilliant bolis 
has been followed in several cases by the fall of aerolites, 
that buried themselves deeply in the earth, and when dug 
out, after some hours, were too warm to be handled. Masses 
of similar structure have been found, partly buried in the 
soil. One in the plain of Otumpa, near Buenos Ayres, was 
7^ feet long, and weighed 33,000 pounds. The aerolite of 



Singular, bolis, from /3olcg; a missile, an arrow. 



AEROLITES. 



271 



Santa Rosa, Fig. 161, reduced to one fifteenth, weighed 1653 
pounds, with a volume of about 3^ cubic feet. 




Fig. 160. — Meteoric Stone from Santa Rosa. 



500. Their nature. — All contain meteoric iron, from 
one or two per cent to ninety or ninety-six per tent. The 
iron is malleable, and may be worked into cutting instru- 
ments. Nickel, phosphorus, silica, lime, and other elements, 
to the number of 22, are also found, but no new element 
has been discovered in them. A polished surface of meteoric 
iron, corroded by diluted nitric acid, shows a crystalline 
structure unlike common iron, but seen in iron o( volcanic 

origin. Systems of parallel lines appear, crossed bv Other 



272 



ELEMENTS OF ASTRONOMY. 



lines at angles of about 60 °, and producing regular trian- 
gular figures. 




Fig. 161. — Section of Meteoric Iron. 

501. Meteoric dust. — Occasional showers of black or 
red dust are thought to have a meteoric origin. The sub- 
stance of shooting-stars which is consumed in the air can not 
be lost or destroyed; though it may become powder of ex- 
ceeding fineness; the powder must finally fall to the earth. 
Dust gathered from mountain-tops has shown traces of iron 
and nickel, which, though comparatively rare in terrestrial 
minerals, are common in aerolites. Meteoric stones, dug hot 
from the earth, have been accompanied by a quantity of black 
powder. In 181 3, a shower of red dust was accompanied 
by aerolites. 

The occurrence of dark days has been explained by sup- 
posing that a stream of meteors passed between the earth 
and the sun, shutting off light and heat for the time. 

THE ZODIACAL LIGHT. 



502. During clear winter and spring evenings a faint tri- 
angular light streams up from the south-west, soon after dark, 
attracting little notice because it seems merely a continuation 
of the twilight that blends with it. Its direction is along the 



THE ZODIACAL LIGHT. 



273 



ecliptic, and its extent usually 20 or 30 degrees; sometimes 
80 or 90 degrees. In October, a similar light precedes the 
sun in the morning, from the south-east. It is best seen in 
these months because its direction is most nearly at right 




Fig. 162. 



angles with the horizon, and it is least obscured by the twi- 
light. In clear nights, between the tropics, it may be traced 
quite across the heavens, forming a complete ring. 

503. Its nature. — It has been suggested that the zodi- 
acal light is caused by a ring of meteoric bodies, which move 
about the sun in sufficient numbers to show a faint light, the 
triangular shape being caused by the obliquity o( the ring. 
The theory more generally accepted is that the ring is com- 
posed of nebulous matter which extends beyond the orbit 
of the Earth, and shines by the reflected light o( the sun. 

Its spectrum is said to give a single yellow line, and, there- 
fore, to indicate a luminous gas. 
Ast.— 18. 



274 ELEMENTS OF ASTRONOMY. 



504. RECAPITULATION. 

Solid masses of mineral substances, like those found in the earth, 
fall from the sky. 

Such masses are known to have come from brilliant meteors which 
passed the earth at a speed so rapid as to show that they were jour- 
neying round the sun. 

The phenomena of shooting-stars indicate a similar nature and the 
same center of motion. 

The number of shooting-stars is infinite; the space of the solar 
system is filled with them, as the air of a summer evening is filled 
with humming insects. 

They move about the sun in eccentric orbits, under the same laws 
which control Jupiter or Xeptune. 



CHAPTER XXL 

THE PROGRESSIVE MOTION OF LIGHT. 

The nature and properties of light are discussed in treatises 
on Optics. Astronomy shows that light moves and finds its 
rate of motion by several independent methods, which give 
results substantially the same. 

505. Eclipses of Jupiter's Satellites. — A telescope 
of moderate power is able at any time to show the moons 
of Jupiter, hence (113) their motions are useful in determin- 
ing terrestrial longitudes. Romer, a Danish astronomer, 





Fig. 163. 



computed the times of their eclipses for a year, beginning 

when the planet was nearest the earth. As the planet moved 
away from the earth, he found that the aetnal time of celipse 
was continually falling behind the time computed, until at 



276 ELEMENTS OF ASTRONOMY. 

conjunction the difference was more than 16 minutes. Be- 
yond this point, as the planets approached, the difference 
diminished, and at opposition had vanished. 

He, therefore, inferred that the 16 minutes was the time 
required for light to cross the earth's orbit; that an observer 
at B would see any event at Jupiter 16 minutes later than 
if he were at A, and proportionately for intermediate dis- 
tances. 

Investigations of the movements of Jupiter's first satellite, 
from 1848 to 1873, gi ye the tnTie required for light to come 
from the sun to the earth as 8 m. 20 sec, or 500 seconds. 
Dividing the distance, 93 millions of miles, we find the 
velocity of light to be 186,000 miles per second. 

So we may observe the phases of a star whose light varies 
regularly, as Algol (546). The real intervals must be equal; 
any annual variation shows the time in which the light 
crosses the earth's orbit. Thus it is possible to compare the 
velocity of the direct light of a star, with that of light 
reflected from a planet. 

506. Aberration. — In 1725, Dr. Bradley began a series 
of observations upon fixed stars, to find, if possible, parallax 
and distance. He found that the stars in opposition to the 
sun, — or, as we would say, those which the earth is passing 
as it moves on in its path, — are moved forward about 20" 
(20.445"), while those in the opposite part of the heavens, 
beyond the sun, are moved backward (in longitude, astro- 
nomically considered) by the same amount ; those toward or 
from which the earth is moving are not displaced. 

The difference in longitude of the same star at different 
seasons of the year amounts to as much as 40", but the 
movement in one direction is balanced by that in the opposite 
direction, returning the star regularly to the same place. The 
relative position of star to star is unchanged, as all in the 
same quarter of the sky are affected similarly. 

This apparent annual displacement of the stars is called 
aberration. 



THE PROGRESSIVE MOTION OF LIGHT. 277 

507. Illustration. — Suppose a rail-car, 10 feet wide, is 
moving at the rate of 30 feet a second; suppose a stone 
thrown at right angles to the track, at a rate of 20 feet a 
second, passes into the car at a window. The stone will 
cross the car in half a second, but during the half second 
the car will have moved forward 15 feet; hence, the stone 













1 


1 

1 
1 


r 


'V. 


~1 '" 




1 
1 
1 


%\ 


±x_ 













Fig. 164. 

will pass out at a point 15 feet nearer to the rear of the car 
than the point where it entered, and that without changing 
its course over the track, and, perhaps, if the windows are 
open, without touching the car at all. To one riding in the 
car, the stone will seem to enter and cross obliquely, and to 
come from some place on the line A'B, rather than on the 
line AB, as was the fact. The apparent obliquity of the 
stone's motion results from the two motions of stone and car. 

508. The velocity of the stone. — The stone left the 
car at a point 15 feet behind that at which it entered, while 
the car was moving 30 feet per second. As the apparent 
backward motion of the stone is really the actual forward 
motion of the car, the time was half a second; in that time 
the stone moved across the car, 10 feet, and its rate of motion 
was therefore 20 feet per second. Evidently we maw if 
more convenient, measure the angle ././'A', and the line .•/'/>, 
and by trigonometry find the sides .//>', and .7.7. from which 
the velocities of both stone and ear may be determined. 



278 



ELEMENTS OF ASTRONOMY. 



509. Application. — Let AB be a telescope which moves 
with the earth, and in a certain time takes the position A ' B '. 
Let a ray of light from the star S meet the object-glass at B, 
and suppose its velocity sufficient to bring it to A at the 

instant that the eye-piece comes 
to the same point. As the ray 
is in the line of collimation at 
B and A, it must have followed 
that line through the tube, and 
there comes to the eye in the 
apparent direction AS', its real 
path having been AS. The 
star is therefore displaced by 
the amount of the angle SAS f 
in the direction of the earth's 
_ motion. 

The angle is 20" (506), and 
the length of the telescope is 
known; the solution of the triangle BAA gives the distances 
AA ', through which the telescope moved, and BA, through 
which the light moved. From the earth's rate of motion, 
the time of passing from A to A is found, which is also the 
time of passage of light from B to A ; hence, the velocity 
of light is determined. 

By this method, Struve finds the time required for light to 
come from the sun to the earth to be 498 sees. ; velocity of 
light, 186,700 miles. 




Fig. 165. 



FIZEAU'S EXPERIMENT. 



510. Theory. — Suppose a wheel which has 1000 teeth in 
its circumference rotates once in a second; evidently the 
time between the passage of two successive teeth is y^Vff of 
a second. If the wheel turns 10 times a second, each tooth 
marks 10 ^ 00 of a second. 



PIZEAU'S EXPERIMENT. 



279 



Suppose a ray of light passes between two teeth of the 
rotating wheel, goes to a mirror at some distance, and is 
reflected back again. If the teeth are passing at the rate of 
10,000 in a second, and the distance is such that the light 
can pass from the wheel to the mirror and back in y-Q^Q-o °f 
a second, the returning 
ray will find the second 
space in the precise 
position for it to pass 
through; but if it occu- 
pies less or more than 
Tffimj- of a second, it 
may find a tooth instead 
of a space, and be in- 
tercepted. 

If the rate of the 
wheel, and the distance 
of the mirror are so ar- 
ranged that the ray will 
pass through the second 
space, doubling the ve- 
locity of the wheel will 
allow the light to pass 

through the third space; two teeth will have passed while the 
light is taking its journey. Three times the velocity causes 
three teeth to pass, etc. 




Fig. 166. 



511. The apparatus. — A telescope, A, is fitted with a 
smaller tube, B, at right angles to the larger. The wheel, 
E, is so placed that its teeth pass through a notch in the tube. 
across the line of collimation of the telescope. The clock- 
work which drives the wheel, ami registers its revolutions, 
is omitted in the figure, for simplicity. A ray of light from 
a lamp passes into the small tube, />', is reflected at C along 
the large tube to a mirror, at a known distance, which 
returns it through the large tube to the observer at D. The 



280 ELEMENTS OF ASTRONOMY. 

observer can see no light which is not reflected from the 
distant mirror. 

When the wheel turns slowly, the reflected rays are all 
intercepted; when the velocity is such that the rays can return 
in the time between the passage of two successive teeth, each 
finds a space to pass through, and goes to the eye, a clear 
bright light like a star. At a more rapid rate, the star van- 
ishes; at double the velocity it re-appears, and again, at three 
and four times the velocity. 

The distance from the telescope to the mirror is twice 
traversed, in a part of a second which is known from the rate 
of the teeth as shown by the clock-work, hence the velocity 
of light is again determined. 

The experiment was made with great care, by M. Fizeau, 
at Paris, and has been repeated by M. Cornu. 

It gave 186,600 miles per second as the velocity of light. 

M. Foucault devised an experiment of a more complicated 
nature by which he obtained the velocity 185,200. 

Foucault's method has been repeated, with some modifica- 
tions, by Michelsen, at the Naval Academy at Annapolis, 
giving velocity 186,382. 



512. RECAPITULATION. 

The velocity of light as determined by 

Miles per second. 

Eclipses of Jupiter's Satellites, 185,770 

Aberration, 186,700 

Fizeau's experiment, 186,600 

Foucault's experiment, 185,200 

Michelsen's experiment, 186,382 

Average, 186,132 

For other reasons, Michelsen's experiment is believed to be most 
reliable. 



CHAPTER XXII. 

THE FIXED STARS. 

513. The fixed stars are those which, to the ordinary 
observer, keep their places with reference to each other, 
They are distinguished from a few which, from their wander- 
ing, were called planets (117). The fixed stars form groups 
nearly the same as those which were seen two thousand years 
ago; careful observations with the telescope, compared after 
the lapse of many years, show that some of them do move. 
Probably none are absolutely fixed in space. Besides keep- 
ing its place, a fixed star usually maintains the same bright- 
ness and color from century to century. 

514. Magnitudes. — The stars are classed by their brill- 
iancy, the brightest being of the first magnitude. Stars larger 
than the seventh magnitude, and, under very favorable cir- 
cumstances, even those of the seventh, may be seen without 
instruments. Smaller, or telescopic, stars are classed as low- 
as the 1 8th, or even the 20th, magnitude. The only limit is 
the power of instruments. 

Sirius is by far the brightest star in the sky, and no other 
is entitled to rank with it. Sixteen to nineteen other bright 
stars are usually classed with Sirius, in the first magnitude, 
although it is not easy to say why the division should be made 
either at the seventeenth, or at the twentieth. 

515. The relative brightness of the magnitudes. — 
Herschel proposed to indicate the relative brightness by 

(-•Si) 



282 ELEMENTS OF ASTRONOMY. 

numbers. He placed two telescopes in such positions that 
he could pass very quickly from one eye-piece to the other. 
He then prepared a series of pasteboard rings, with openings 
of various sizes; with these rings, laid over the object-glass, 
he could admit more or less light, as he pleased. When 
comparing two stars, he reduced the light of the brighter 
until it seemed no more than that of the less. Then he 
considered that the magnitude of the stars were propor- 
tioned inversely to the areas through which their lights were 
received. 

Thus, when he covered three fourths of the object-glass, 
Arcturus, a star of the ist mag., seemed no brighter than 
Polaris, of the 2d mag. ; hence, Polaris is one fourth as 
bright as Arcturus. In the same way, Polaris is found equal 
to four times Mu Pegasus, of the 4th mag., and Mu Pegasus 
is equal to four times q Pegasus, which is between the 5th 
and 6th mags. Hence, the brightness of Arcturus is 

4 times that of a star of the 2d mag. ; 
16 times that of a star of the 4th mag.; 
64 times that of a star between the 5 th and 6th mag. 

Working by this method, he found the average brightness 
of the magnitudes as follows: 

Sirius, brightness 320. 



Mag. 


Av. bright. 


No. of stars. 


Mag. 


Av. 


bright. 


No. of stars. 


I 


IOO 


20 


4 




6 


300 


2 


25 


40 


5 




2 


IOOO 


3 


12 


I50 


6 




1 


4500 



Zollner compares the light and color of a star with an 
artificial star, whose light can be varied at pleasure. The 
results of this method are yet to be published. 

516. The number of the stars. — In the whole heavens, 
about 6000 (5905) stars may be seen without a telescope. 



CONSTELLATIONS. 283 

As but half the sky is visible at once, and only the brightest 
stars can be distinguished within several degrees of the hori- 
zon, probably not more than 2500 can be seen at once. 
That the "stars of heaven" should seem to be "countless," 
is due partly to their irregular distribution, and partly to our 
inability to comprehend, and, therefore, to apply, large num- 
bers. The number of a body of soldiers always seems less 
when the men are in order, than when scattered; the number 
of persons in a crowd is always overrated. 

The number of stars above the 10th mag. is placed at 
about 200,000, while it is estimated that more than 20 mill- 
ions are visible with Herschel's 18-inch reflector. Instruments 
of greater power reveal yet greater multitudes. The number 
of stars in the universe is beyond the conception of the human 
intellect — is infinite. 



CON ST ELLA TIONS. 

517. In early ages, the groups of stars received names 
which have been retained to the present time. Some, as the 
Bear and the Bull, came from a fancied resemblance to the 
forms of those animals in the outlines of the groups; most 
were derived from the ancient mythologies — from gods 
or heroes, who left the earth and were transfigured in the 
skies. 

518. Modern constellations. — The part of the sky 
about the south pole was not known to ancient astronomers. 
The outlines of the old constellations did not exactly fit each 
other, and many patches of sky lay between, which did not 
belong to any. From these two sources, modem astronomers 
formed new groups, to which, from motives o\ gratitude, of 
flattery, or of caprice, they gave names of distinguished men. 
of princes, of animals, or of scientific instruments. 

The whole number of recognized constellations is 1 1;. 



284 ELEMENTS OF ASTRONOMY. 

519. The Zodiac. — Twelve constellations along the 
ecliptic, extend about eight degrees on either side, forming 
a belt 16 degrees wide, called the Zodiac* They are 

Aries, the Ram; Libra, the Scales; 

Taurus, the Bull; Scorpio, the Scorpion; 

Gemini, the Twins; Sagittarius, the Archer; 

Cancer, the Crab; Capricornus, the Goat; 

Leo, the Lion; Aquarius, the Waterman; 

Virgo, the Virgin; Pisces, the Fishes. 

520. The signs of the Zodiac. — Although these con- 
stellations occupied the entire circuit of the sky, they did 
not divide it equally. The zodiac was therefore divided into 
12 equal parts, called signs, each 30 in extent. To each 
sign was given the name of the constellation which lay mostly 
within it. Thus, the first sign, which extended 30 from the 
vernal equinox, was called Aries, because, when the zodiac 
was divided, it contained the constellation Aries. 

521. The signs have moved backward. — The vernal 
equinox moves backward, or westward, along the ecliptic, 
about 50" a year, the autumnal equinox following at 180 . 
The equinoxes seem, therefore, to go toward the sun; their 
motion is called the precession of the equinoxes (App. V). 
Since the division of the zodiac, the equinoxes have moved 
about 2 8°, and the sign Aries now contains the cofistellation 
Pisces. 

The number of seconds in the zodiac, divided by the an- 
nual motion of the equinox, gives the time in which it will 
make the entire circuit of the sky; it is about 26,000 (25,870) 
years. From a similar computation, La Place supposes that 
the division of the zodiac into signs was made about 2500 
years b. c. 



* Greek, ZuSiano-, zodiakos (/ct'/c/lor, kuklos, a circle, understood), 
meaning a ring of animals. 



CONSTELLA TIONS. 



285 



522. The northern constellations. — The most notable 



Andromeda; 
Aquila, the Eagle; 
Auriga, the Wagoner; 
Corona Borealis, the North- 
ern Crown; 
Cygnus, the Swan; 
Draco, the Dragon; 
Hercules; 
Lyra, the Lyre; 



Bootes , 

Cassiopeia ; 

Cepheus; 

Ophiuchus; 

Pegasus, the Winged Horse; 

Perseus; 

Ursa Major, the Great Bear; 

Ursa Minor, the Little Bear. 



523. The southern constellations. — The principal are 



Argo Navis, the Ship Argo ; 
Canis Major, the Great Dog; 
Canis Minor, the Little Dog; 
Centaurus, the Centaur; 
Cetus, the Whale; 
Crux, the Cross; 



Eridanus; 

Monoceros, the Unicorn; 
Orion; 

Piscis Australis, the South- 
ern Fish. 



524. Names of the stars. — After the constellations 
were named, it was usual to indicate a star by the place 
which it occupies, as, the Lion's heart, the Bull's eve, the 
ear of Virgo, the girdle of Orion. Many of the brighter 
stars have names of Latin, Greek, or Arabic derivation. 
Such are Regulus, Capella; Sirius, Arcturus; Aldebaran, 
Algol. 

525. The stars indicated by letters. — In 1604, Bayer, 

a German, published maps of the sky, in which the stars of a 
given constellation were indicated by the letters o( the Greek 
alphabet, the brightest being a, alpha; the next, \ beta; the 
third, }', gamma, and so on. When the 24 Greek letters 
were exhausted, he used the Roman letters, and then num- 
bers. 'Thus, a Draconis, means the brightest star in the 
Dragon; > l'ersei, the second star in Perseus; b Ononis, 



286 ELEMENTS OF ASTRONOMY. 

the 26th of Orion; 61 Cygni, the 111th of the Swan. It 
appears that Bayer did not indicate the order of the stars 
from any observations of his own, but according to their 
magnitudes as given by Ptolemy and Tycho Brahe. The 
letters do not now always give the order of brightness ; as an 
example, either j3 or 7 Draconis, is brighter than a of the 
same constellation. 

526. Catalogues of stars. — Several have been made, 
the stars being entered by right ascension and declination, 
in the order of right ascension. The first, by Hipparchus, 
B. c. 128, contains 1025 stars. 

Among the most important modern catalogues are the 
following : 



Name 


Date. 


No. Stars. 


The British Association, 


1845. 


8,377 


Lalande's, 


1801, 


47,39° 


Bessel's, 


1846-63, 


62,000 


The zones of Argelander, 


1859-62, 


324,000 



References are made by the name of the catalogue and 
the number of the star. 



NATURE OF THE STARS. 



527. The stars are suns. — The polariscope shows that 
the light of stars has not been reflected; they are, therefore, 
self-luminous. But the only self-luminous body which we 
know in the sky is the sun; hence, we conclude that the 
stars are suns, and that the sun of our system shines as a star, 
if seen at a like distance. We may farther suppose that the 
stars, like our sun, are centers about which systems of planets, 
satellites, and comets, revolve. We shall find reason to be- 
lieve that some of the stellar systems are far more compli- 
cated and wonderful than our own. 



NATURE OF THE STARS. 287 

The stellar light, analyzed by the spectroscope, indicates 
that elements exist in the stars which are identical with those 
found in the sun and in our earth, together with others un- 
known in either sun or earth, materials utterly unknown and 
inconceivable. 

528. Stars in the telescope. — To the naked eye, a star 
is a bright point surrounded by rays. The telescope cuts off 
the rays, and so diminishes the apparent breadth, while it 
increases the brightness. A planet shows a disc, like a little 
moon; a star does not. 

The brighter stars, in the best telescopes, seem to be ex- 
ceptions ; but the disc in these cases is believed to be caused 
by the dispersion of light in our atmosphere, and not to be 
real. If a disc of appreciable breadth were really seen, it 
should increase with higher magnifying power; when hidden 
by the moon, the star should vanish at the moon's edge 
gradually, rather than instantly as is the fact. 

529. How are the stars visible ? — They show no disc. 
They are, therefore, seen only by the intensity of their light. 
The star is at the center of a sphere which it fills with light that 
diminishes in intensity as the square of the distance increases. 
The pupil of the eye admits a certain amount of this light, and 
the lenses condense it upon the sensitive retina. If the con- 
densed beam is intense enough, it excites the nerve, and we 
see the star ; if not, the star is invisible. 

The telescope, by its object-glass, or its speculum, gathers 
up as much more light as its cross-section is larger than the 
pupil of the eye. This greater amount of Light, condensed 
by the lenses and passed to the eye, may be intense enough 
to make itself visible; thus the telescope reveals stars which 
the unassisted eye can not see. 

530. 'Why do stars differ in brightness? — By differ- 
ence in distance, and difference in size. It' the sun were 
twice as far from us as now. its light would be one fourth as 
intense; at three times the distance, the light would be 1 ; at 



288 ELEMENTS OF ASTRONOMY. 

ten times, y^, etc. The proof is precisely the same as that 
for varied attraction of gravitation (157). If the stars are 
suns of equal size and brilliancy, those that are brightest 
must be nearest, and conversely, according to the law. But 
among the nearest fixed stars are some of small magnitude. 
We, therefore, conclude that the different glory of the stars 
depends upon both size and distance. 

531. Their brilliancy compared with that of the 
sun. — Wollaston found that the sun's light is 800,000 times 
that of the full moon, and that is 27,000 times the light of 
the star Alpha Centauri, of the first magnitude. Hence, at 
the earth, the sun's light is 21,600 million times that of Alpha 
Centauri. But that star is 224,000 times as far away as the 
sun; if it were brought as near as the sun, its light would 
appear 224, ooo 2 = 50,176 million times as great as now, or 
about 2.4 times that of the sun. 

In a similar way, we find that Sirius is a center of light 
and heat 393.7 times larger and grander than our sun. 



DISTANCES TO THE STARS. 

532. The distances to some of the fixed stars may be 
found approximately by methods similar to those explained 
in Chap. IX. 

Frequent measurements with the micrometer show that the 
distances between some of the fixed stars and their neighbors 
are variable. A star that is near the ecliptic seems to move 
back and forth on a short line annually. Another, near the 
pole of the ecliptic, describes a small circle; and others, 
between the ecliptic and its pole, move in ellipses which are 
flattest when nearest the ecliptic. 

The cause of this apparent motion can be neither refraction 
nor aberration (506), because either of these would affect 
alike all the stars in the same part of the sky. When one 



DISTANCES TO THE STARS. 



star appears to approach another, and then to recede from 
it, annually, we suppose, first, that the apparent motion is 
caused by the actual annual motion of the earth in its orbit; 
second, that the star which seems to 
move is much nearer than that which 
appears stationary. 

The base-line (Fig. 167) is now the 
axis of the earth's orbit, and the angle 
of parallax is the angular motion of the 
star during half a year. 

533. Results. — As our measuring 
rod is now the radius of the earth's 
orbit, our results will be in that denomi- 
nation. We may express them in mill- 
ions of millions of miles, but these 
numbers are beyond our grasp. By 
walking nearly 30 miles a day, a man 
might travel 10,000 miles in a year, or 
one million miles in 100 years. At that 
rate, the journey to the sun would re- 
quire 9300 years; if Adam had begun 
at his creation and traveled until now, 
he would have completed less than two 
thirds of his task ! How shall we com- 
prehend distances whose unit of measure 
is so vast? 




earth's orbit. 



Fig. 167. 



534. Alpha Centauri. — This star has an annual parallax 
of 0.92". This gives a distance of 224,000 times the ratlins 
of the earth's orbit, or 20,832,000 millions of miles. At 30 
miles an hour, a rail-car will run 263,000 miles in a year — a 
little farther than to the moon. The ear must continue its 
unvarying speed for about 80 millions of years to reach this 
star. \ cannon-ball, flying at the rate of 1 mile in 5 seconds. 
would expend 3,300,000 years in the journey. Finally, light 
itself, the swiftest agent we know, which traverses [86,000 

A st. —19. 



290 ELEMENTS OF ASTRONOMY. 

miles in a single second, will have been more than 3^ (3-55) 
years in coming from Alpha Centauri to our eyes. 

Yet Alpha Centauri, so far as we know, is our nearest 
neighbor among the stars. 

535. Other stars of known parallax. — The times and 
distances in the following table, from Arago, for four of the 
nearest fixed stars are not supposed to be exact. They are 
only the smallest round numbers which the conditions of the 
problem admit. 





Distance 


from earth, in 


Time 


required for pas- 


Star. millions 


of 


millions 


of miles. 


sage 


of light, in years. 


Alpha Centauri, 






20 






3-* 


Sirius, 






127 






21.5 


Arcturus, 






152 






2 5-5 


Polaris, 






286 






48.3 



536. Distances of smaller stars. —We may reason- 
ably suppose that some, even of the smallest telescopic stars, 
are, in fact, bodies as large as Alpha Centauri, and seem 
small by reason of their greater distance. Referring again 
to Herschel's method of comparing the brightness of stars, 
and remembering that the intensity of light diminishes as the 
square of the distance increases, we find that, at twice its 
present distance, Arcturus, a star of the 1st magnitude, some- 
what less than Alpha Centauri, would be as bright as a star 
of only the 2d mag. ; at four times its distance, it would 
appear of the 4th mag. ; at twelve times its distance, of the 
6th mag. Hence, we suppose that some stars of the 6th 
mag. are at least twelve times as remote as Alpha Centauri, 
and that their light is at least 43 years in coming to the 
earth. 

Evidently much greater results would come from a com- 
parison with Sirius or Polaris. 

537. Distance of telescopic stars. — A star of the 6th 
mag. is just visible to the naked eye. A telescope whose 
object-glass has twice the diameter of the eye-pupil, has four 



VARIATIONS OF STARS. 291 

times the area, and admits four times the light; it will, there- 
fore, reveal a star which is twice as distant as a star of the 
6th mag. So one of three times the diameter of the eye- 
pupil, wouk} show a star three times as far away. 

The pupil of the eye is ordinarily about one eighth of an 
inch in diameter; the object-glass of the great Washington 
refractor has an opening of 26 inches, or 208 eighths of an 
inch. Hence, the Washington refractor will show a star of 
the actual size of Alpha Centauri, when removed 208 times 
as far as a star of the 6th magnitude; and the light of that 
star would require more than 208 X 43 years, or more than 
8900 years, in coming to our eyes. Were such a star blotted 
from the firmament when Adam began to till the soil of 
Eden, the last installment of its expiring light, now on the 
way, would not yet have reached the earth. 

538. Results. — Light occupies, in coming to the earth 
from the nearest star of the 

1st mag., more than 3.6 years. 

2d " of same actual size, 7.2 " 

4th " " " 14.4 " 

6th " " " 43. 

From smallest stars in Washington refractor, 8900. " 

Immense as these distances seem, astronomy teaches of yet 
greater depths of space. 

VARIATIONS OF STARS. 

539. They have become less bright. — Eratosthenes 

says of the stars in the scorpion, "they are preceded by the 
most brilliant of all, the bright star o\ the northern claw." 
The star of the southern claw is now brighter than that of the 
northern, while Antarcs, of the same constellation, is brighter 
than either. Stars which Flamsteed and Bayer recorded in 
their catalogues as of certain magnitudes, are ik>w classed 
in much smaller magnitudes. 



292 ELEMENTS OF ASTRONOMY. 

540. Stars have vanished. — Many stars of the old 
catalogues can not now be found; probably most of these 
entries were erroneous, but some stars are known to have 
disappeared. The 55th of Hercules was recorded by Bayer 
as of the 5th mag. In 1781, Herschel saw it and noted its 
red color in his journal. In 1782, he noted it again. In 
1 791, he saw no trace of it, and it has not since been seen. 

541. They have become more brilliant. — Several 
stars in Flamsteed's catalogues are classed in higher magni- 
tudes by Herschel. A small star near Mizar, the middle 
star of the handle of the Dipper, was called Saidak, the proofs 
by the Arabs, because the ability to see it was a test of very 
keen eyesight. It is now easily seen. 

542. Variations of color. — Single stars show great 
variety of color, running through shades of red, yellow, blue, 
and green. Some have changed color. Sirius, which ancient 
astronomers describe particularly as red, has to modern ob- 
servers shone with purest white, and of late shows a light 
emerald green. Aldebaran, Antares, and Betelgeuze are 
red ; Arcturus is orange ; Capella, bluish. How strange would 
the world appear to human eyes, if the sun should shed only 
blue, red, or orange light! 

543. Stars have appeared. — The appearance of a new 
star is said to have suggested to Hipparchus the idea of 
making a catalogue of the stars. This statement was sup- 
posed to be mere fiction until the appearance of the same 
star was found recorded in the Chinese annals. 

New star of 1572. — This star, observed by Tycho 
Brahe, November 11, appeared in the constellation Cassi- 
opeia. In size, it surpassed Sirius, and it could be compared 
with Venus when she is brightest. It was seen in the day- 
time, and at night through clouds of considerable density. 
Its position was carefully found, to make sure that it did not 
move, and was not a comet. In December its brightness 



VARIATIONS OF STARS. 293 

began to diminish, and it gradually passed through the de- 
grees of brightness until March, 1574, when it vanished, 
having been visible seventeen months. Its color was first 
white, then yellow, finally red. 

544. Other new stars. — A temporary star appeared in 
Ophiuchus, in October, 1604. In November it was brighter 
than Jupiter. It gradually diminished, and after remaining 
visible fifteen months disappeared. 

In 1848, Mr. Hind observed a new star in Ophiuchus; 
after a few weeks, it waned from the 4th to the 12th mag. 

In May, 1866, a star of the 2d magnitude appeared in the 
Northern Crown; in June, it was of the 9th mag. Many 
other instances might be cited. 

545. Periodic stars increase and diminish in brightness 
at regular intervals. About 100 are known, having periods 
which vary from a few days to many years. Stars which 
have become more or less brilliant, and even the temporary 
stars, may yet be found to be periodic. 

546. Algol. — This most remarkable of all the periodic 
stars, also called Beta Persei, is in the head of Medusa. It 
is of the 2d mag. for 2 days 13 hours; it then changes, in 
3^ hours, to the 4th mag. ; and in 3^ hours more, returns 
to its former brightness. Its entire period is about 3 days 
(2 d. 20 h. 48 m. 55 s.). Its variation has been observed 
about 200 years. 

547. Mira. — Because of its variation Omicron Ceti was 
named Mira, The Wonderful. This star is of the 2d mag. 

for about 14 days; it then diminishes until, after about two 
months, it is invisible without a glass, being of the oth or 
10th mag. After six or seven months it re-appears, and in 
two months more recovers its greatest si/e. It makes this 
circuit on an average of about 331 days; but the period varies 
about 25 days in 88 changes. 



294 ELEMENTS OF ASTRONOMY. 

548. The causes of these periodic changes are not 
known. Several theories have been suggested. 

1. That the star is a body which, like the sun. has many 
dark spots, or which emits light from only one side, and that 
it rotates, presenting alternately its bright and dark sides. 

2. That the rotating body is flat like a millstone, and 
presents first its broad surface, then its edge. 

3. That a dark body, or planet, revolves about the bright 
central body, and thus shuts off the light. 

4. That a nebulous mass revolves about the star, gradually 
intercepting the rays, and as gradually restoring them. This 
theory has fewest objections. 

5. Newton suggested that a body, before invisible, had 
been set on fire by collision with a comet, and remained 
visible until consumed. 



DOUBLE STARS. 

549. Although all stars seem single to the naked eye, the 
telescope resolves many into two, and some into several, 
distinct bodies. In 1780, Herschel knew but four double 
stars. He increased the number to 500, and now many thou- 
sands have been entered in star catalogues. 

Some are separated by telescopes of low power, others 
require instruments of great power, and of very delicate 
definition. The most important part of a refractor is its 
object-glass. If its surfaces are accurately ground and pol- 
ished, and its material is of equal density throughout, this 
glass gathers all the light which passes through it into a single 
point, the focus. An imperfection in either respect causes 
some rays to fall short of the focus, or beyond it, and the 
image is a little indistinct. The eye-piece can not cure this 
defect; it can only magnify the imperfect image. This exact 
defining power is the precise quality needed to resolve some 
of the double stars; there must be entire absence of blur. 



DOUBLE STARS. 295 

550. Stars optically double. — The components of a 
double star may be only apparently near; one may be far 
beyond the other, in almost the same line of sight. Indeed, 
one may conceal another which is exactly behind it. But 
such apparent nearness of bodies which have no relation to 
each other could not often occur. 

551. Binary stars. — Herschel, supposing that double 
stars were only optically double, expected that they would 
give fine opportunities for observing annual parallax, and 
thus for finding distances. He soon found that, in most 
cases, each has the same apparent annual motion, and, hence, 
that the two must be about equally distant. After about 
twenty years' labor, he could say that in certain cases one 
component describes an orbit about the other, thus proving 
a physical relationship. A star which is single to ordinary 
vision, but which may be resolved into two stars thus 
physically related, is a physically double, or binary star. 

552. The components of the same star are rarely of 
the same brightness or color. The parts of Alpha Centauri 
are of the 1st and 2d magnitudes; of Gamma Virginis are 
each of the 4th; of 70 Ophiuchus, 4th and 7th; of Polaris, 
2d and 9th. The colors of some double stars are comple- 
mentary, that is, such as together produce white light. A 
faint white near strong red often seems green; if the near 
and strong light is yellow, the white light appears blue. 
Many of the pairs of color can not be explained by contrast. 
From a long list a few are selected. 

Star. Color of large member. Color of small member. 



Gamma Andromedae, 


Orange, 




Sea green. 


Alpha Piscium, 


Pale Green. 


Blue. 


Eta Cassiopeise, 


Yellow, 




Purple. 


Zeta Coronae. 


White, 




Light Purple 


Kappa Argus, 


Blue, 




Park Red. 


Star in Centauries, 


Scarlet, 




Scarlet. 


lota Cancri, 


Bright V 


ellow. 


Indigo lUue. 



296 



ELEMENTS OF ASTRONOMY. 



553. Revolution. — We have already remarked that one 
of the components of a star physically double moves about 




Fig. 168. 

the other. The diagram, Fig. 168, shows the observed po- 
sitions of the two parts of Gamma Virginis ; and Fig. 169, 
the orbit derived from these observations. In Fig. 169, in 



1836 





Fig. 170. — 70 Ophiuchi 



1756 

Fig. 169. — Gamma Virginis. 

Fig. 170, 70 Ophiuchi, and in Fig. 171, Alpha Centauri, the 
full line shows the true shape of the orbit, while a dotted 
line shows the orbit as seen from the earth, obliquely. 

554. Time of revolution. — Of the stars known to be 
physically double, twelve have periods less than a century; 




PLATE III.— i, Star Cluster in Hercules. 2, in Libra. 3, in the Toucan. 4, in 
Pegasus. 5, in Canes Venatici. 6, in Cepheus. 7, Theta Orionis. 8, in Capricorn, 
9, Eta Lyrae. F. 297, 



MULTIPLE STARS. 



297 



about 400 seem to require more than 1000 years to complete 
a single revolution. The time during which these stars have 




Fig. 171. — Orbit of companion to Alpha Centauri 



been studied is too short to admit an accurate determination 
of their periods. Probably most of the double stars will 
prove to be physically connected. 
The periods of a few are: 

Zeta Herculis, 35 years. 

Sirius, 50 

Xi Ursae Majoris, 63 

Alpha Centauri, 77 

70 Ophiuchi, 93 

Gamma Virginis, 182 

61 Cygni, 452 



MULTIPLE STARS. 



555. Zeta Cancri. — This star has 
three members, two of which revolve 
about the third. Since 1782, the 
nearer of the companions has made 
nearly two complete revolutions, the 
period being 58 years ; the more dis- 
tant has passed over rather more than 
37 of its orbit, indicating a period of 
more than 500 years. 

556. Theta Orionis. — A ^ood 
telescope resolves this star into four 
Components, arranged as in Fig. 7 

of Plate III.; instruments of higher 



1782 



L864* 




PI 



K- 17*- 



Zeta Cancri. 



298 ELEMENTS OF ASTRONOMY. 

power show that each of the two lower stars has a companion, 
and of late a seventh star has been found in the group. 
It does not yet appear that these stars are physically con- 
nected; they do not appear to have changed their relative 
position since they were first observed by Herschel. 

557. The stars obey the laws of gravitation. — The 

members of such binary and ternary systems as have motion 
are found to obey the great laws of Kepler. The orbits in 
which they revolve are ellipses; the radii vectores describe 
equal areas in equal times. Thus it appears that the laws of 
gravitation and of planetary motions are indeed universal. 

The companions of Alpha Centauri and Gamma Virginis 
move in orbits which are very eccentric ; more than those 
of any of the planets in our system. 

The motions of certain stars, Procyon for example, indicate 
the presence of companions or satellites as yet invisible. 

558. Dimensions of stellar orbits. — The distance of 
Alpha Centauri is believed to be about 224,000 times the 
distance of the sun. The orbit of its companion has a major 
axis which subtends an angle of 30"; from this it appears 
that the mean radius of this orbit is about 16 times the mean 
radius of the earth's orbit, or about 1488 millions of miles- 
four fifths the distance of Uranus from the sun. 

The radius of the orbit of the companion of 61 Cygni is 
about 44 times that of the earth's orbit, or about 4000 mill- 
ions of miles. Its orbit is considerably larger than that of 
Neptune. 

559. Masses of the double stars. — We apply to the 
stars whose companions move at known distances the same 
method for finding mass which was used in finding the mass 
of Jupiter, or of any planet which has a satellite. From 
this it appears that the sum of the masses of components of 
the star of Alpha Centauri is 0.7 that of the sun; 61 Cygni, 
0.3 that of the sun; 70 Ophiuchi, about 3 times the sun. 
Thus does the astronomer weigh even the stars in a balance. 



CLUSTERS OF STARS. 299 



CLUSTERS OF STARS. 



560. The Pleiades, or Seven Stars, is a noted cluster in 
the neck of Taurus. Six stars may be easily counted, and 
glimpses of many more may be seen with the naked eye; 
some persons distinguish twelve or fourteen. The telescope 
shows about an hundred. The largest star, Alcyone, is near 
the ecliptic. Certain theorists have supposed that the center 
of the universe is in this star, and that solar and stellar sys- 
tems revolve about it; the theory is not sustained by astro- 
nomical research. 

The Greeks called this group the Pleiades, from their 
word pletn, to sail, because the Mediterranean was navigable 
without danger, when they rose and set nearly with the sun. 

561. Other clusters of note. — A bright spot in Cancer, 
called Praesepe, or the Manger, is resolved by the telescope 
into a cluster of stars. 

A cluster in Hercules, which to the naked eye shows a 
hazy spot of light, makes a magnificent display when viewed 
with a powerful telescope. The stars are scattered somewhat 
thinly near the edge of a nearly circular space, but growing 
more numerous toward the center, blaze there, a dense mass 
of most brilliant gems (Plate III., Fig. 1). 

In Centaurus a still richer cluster is found. Without the 
telescope, it seems a hazy star of the 4th magnitude ; but in 
the instrument, it appears a globular mass of stars, too nu- 
merous to count, and covering a space two thirds as broad as 
the moon. 

The most beautiful specimen is the splendid cluster in 
Toucan (Plate III., Fig. 3), in a region o( the southern sky 
quite devoid of stars. There are three distinct gradations 
of light about the center; the orange red color o( the central 
mass contrasts wonderfully with the white light oi the con- 
centric envelopes. 



300 ELEMENTS OF ASTRONOMY. 

562. Astral systems. — We must believe that the stars 
in these groups are within the sphere of mutual attraction; 
they must, therefore, be in motion. But their distance from 
us is so great, that the separate stars of which they are com- 
posed may be as far apart as the sun is distant from the 
nearest fixed star. These clusters are, then, grand systems 
of suns, moving in harmony about one common center. 
We may call them astral systems. 



NEBULM. 

563. The word nebula means a mist or cloud. In 
1682, Simon Marius observed in the constellation Andromeda 
a spot about 2^4° long by i° broad, which gives a dim light 
like "that of a candle seen through a thin plate of horn." 
Huyghens found another such spot in the sword of Orion. 
Because the light from these spots is misty, they are called 
nebula, clouds. 

As the making of star catalogues progressed, more were 
discovered, while each improvement of the telescope has 
revealed yet greater numbers. Herschel noted over 2500, 
and more than 5000 are now recorded. 

564. Appearance. — Nebulae are faint patches of light, 
with the same ragged outlines which star-clusters show to the 
naked eye. The telescope resolves many into clusters; each 
more powerful instrument, while it discovers new nebulae, 
resolves some of those before known. Some show a ground 
of nebulous light studded with stars. Others, and among 
them some of the longest known and most carefully observed, 
have resisted the highest powers, and the most accurate 
definition. 

565. The spectroscope. — As one nebula after another 
was resolved by the telescope, many were led to suppose that 
all would yield to suitable instruments, that all nebulae are 
clusters of stars. 




PLATE IV.— i, Nebula in Andromeda. 2, in Ursa Major. 3, in the Virgin. 4, Great 
Spiral in Canes Venatici. 5, in Lyra (Herschel). 6, the same m Lyra (Lord Rosse). 7, 
in the Unicorn. F. 301. 



NEBULM. 301 

In 1864, Mr. Huggins analyzed the light from a nebula 
in Draco, and found that it is not compound, like sunlight, 
but that the rays come from a glowing gaseous substance, 
devoid of any atmosphere. The lines in the spectrum indi- 
cate the existence of hydrogen, nitrogen, and a third sub- 
stance not recognized. 

Hence, it seems certain that some nebulae are not star- 
clusters, and that no delicacy of instrument can ever resolve 
them. They may be much nearer than has hitherto been 
supposed. 

566. Their forms are various. Even the same nebula 
shows very different shapes in instruments of different 
powers. 

The spherical are most common. These have a cir- 
cular outline, from which the light gradually increases toward 
the center; they resemble star-clusters. When a bright point 
appears in the center, the nebulae is a nebulous sta?' ; if the 
light is quite equally diffused over the whole disc, it is a 
planetaiy nebula. 

567. Elliptical. — Some have an elliptical outline like 
that of a disc seen obliquely. The great nebula of Androm- 
eda (Plate IV., Fig. 1) is shaped like a convex lens seen 
edgewise. One near Cygnus has an oval outline, surround- 
ing a brighter figure somewhat resembling a dumb-bell. 

568. Annular. — A nebula in Lyra shows an oval ring 
which surrounds a space of fainter light, as if thin gauze 
were stretched across the ring. Lord Rosses telescope 
resolves the ring into bright points, and shows faint bands 
of light across the opening; the ring seems bordered with a 
fringe. Other rings show two bright points at opposite ends 
of a diameter. Another has the ring drawn out into a nar- 
row ellipse, and the two bright points are at the ends o\ the 
opening (Plate [V., Figs. 5 and (>). 

569. Spiral.- — A nebula in Canis Venatici shows to Her 
schel II. a large bright globular cluster, surrounded by .1 ring 



302 ELEMENTS OF ASTRONOMY. 

at a considerable distance from the globe, varying much in 
brightness, and for about two fifths of its circumference 
divided into two parts, one of which appears raised up from 
the other; near it is a small bright globe. Lord Rosse's 
telescope reveals splendid lines of light which pass spirally 
from the central globe to the ring, while other spiral lines 
connect the outer globe with the rest of the system. The 
whole is thickly strewn with stars (Plate IV., Fig. 4). 

A nebula in Virgo shows a bright central spot, like the 
nucleus of a comet, surrounded by four broad spiral branches 
like tails, each being divided by dark lines into numerous 
spiral threads. 

The spiral nebulae now known number about 40, and as 
many more are supposed to have this form. 

570. Irregular. — Most nebulae are included in some of 
the foregoing classes, whose regular forms indicate some 
central force of attraction, and, consequently, some motion 
of the parts. A few are too irregular, so far as they are yet 
observed, to indicate any such conformity to law. 

The lens-shaped appearance of the nebula of Andromeda, 
already mentioned (563), is changed under high powers into 
the irregular outline in Fig. 2, of Plate V. Two dark fur- 
rows seem to have been plowed through the middle of it, 
and the whole surface is sown broadcast with stars. 

The Dumb-bell nebula (Plate V., Fig. 3) also shows a 
profusion of stars, under high powers. The general outline 
is the same as with low powers, but the bright inner figure 
is much changed. 

A nebula in Taurus (Plate V., Fig. 1) is oval in ordinary 
telescopes; in Lord Rosse's reflector it resembles a huge 
crab, with legs formed of strings of stars. 

The nebula of Orion is too irregular to be described. The 
drawings of Bond, Struve, and Secchi show that it has 
changed considerably since it was first figured by Herschel. 
Struve says that the central part is continually agitated like 
the surface of the sea. 



THE MILKY WAY. 303 

Other nebulae are as irregular and as ill-defined as a mottled 
summer-cloud, and the causes which determine their shape 
can be as little understood. 

571. Nebulous stars are masses of nebulous light sur- 
rounding one or more bright points (566). Some have a 
single point at the center; others, a point at each focus of 
the curve of outline ; one has three at the angles of an equi- 
lateral triangle ; a long nebula has two stars at the ends of its 
longest diameter. 

These points are supposed to be centers about which the 
nebulous matter is accumulating. They have also been 
thought to be suns surrounded by dense atmospheres, made 
visible by the transmitted light, as a fog becomes visible 
about a lamp. 

572. Double nebulae. — As we find double and multiple 
stars, so we find double and multiple nebulae. In these 
grouped lights, are seen the same varieties of form which 
appear in the single nebulae. We find associated two globular 
masses; two elliptical masses; an elliptical with a globular 
mass (Plate V., Pig. 7); two globes surrounded by bright 
arcs, like fragments of a broken ring (Plate V., Fig. 6); 
and, finally, a large elliptical mass of light, on whose outer 
edge are scattered, not very regularly, seven smaller globose 
masses, as small bunches are seen growing on a larger potato 
(Plate V., Fig. 5). 

THE MILKY WAY. 

573. The names, (inlaw from the Greek, Ma Lactea 

from the Latin, and our own Milky Way, all refer to the 
broad white band which traverses the entire circuit o\ the 
sky. The Chinese call it The Celestial River; the North 
American Indians, The Road oi Souls. 

574. Its course is in a great circle inclined about 63 ° 
to the equinoctial, which it crosses in the Eagle and in the 



304 ELEMENTS OF ASTRONOMY. 

Unicorn. Beginning near the Eagle, we trace it north- 
east through Cassiopeia, to the right of Capella and Procyon, 
and to the left of Orion and Sirius; thence it passes through 
the Ship, and so beyond our horizon. Beyond Argo it 
divides into several fan-like branches, which unite again near 
the Cross. Beyond the Centaur, it divides into two streams, 
which flow side by side through the Scorpion, Sagittarius, 
and the Eagle, to the place of beginning. 

575. Its breadth and brightness. — Near the Cross, 
where it is narrowest, it is only three or four degrees wide. 
At the Ship, and also at the Scorpion, it spreads over about 
twenty degrees of the sky. The brightest part in the north 
is near the Eagle and the Swan; the part in the south, be- 
tween the Ship and the Altar, is yet more brilliant. Near 
this ' southern portion is a series of the brightest stars in the 
sky, beginning with Sirius, and including the beautiful stars 
of the Ship, the Cross, the Centaur, and the Scorpion. When 
this part of the sky rises above the southern horizon it brings 
a glow of light like that of the new moon. 

576. The telescope resolves the galaxy into countless 
multitudes of stars, irregularly grouped. Star-clusters are 
very numerous, especially in the southern part. In some 
regions the stars are strewn very uniformly, in others a rapid 
succession of closely clustering, rich patches are separated 
by comparatively poor intervals, or, in some instances, by 
spaces quite dark and devoid of any star, even of the smallest 
telescopic magnitude. 

A bright portion near the Cross surrounds a dark place of 
considerable breadth, and of pear-shaped form, called the 
coal sack. Similar spaces are found in the Scorpion, and in 
Ophiuchus. They are like windows opened through the 
dense wall of stars, through which we look forth into vast 
regions of starless space. 

In many places the galaxy is so completely resolved by 
the telescope that the stars seem to shine out against a 




v „ P xA TI ? y-Tr\ Cvah , Nebul « ', n Taurus, b. Creat Nebula in Andromeda, j. Dumb- 
bell Nebula in Vulpecula j. Nebula in Leo. 5. Multiple Nebula in Nubecula Major. 

6. Double Nebula. 7 . Nebula in c oma Berenices. 



THEORIES OF THE GALAXY. 305 

black ground; in others a faint white glimmer remains un- 
resolved, showing that in these directions it has not yet 
been fathomed. 

577. The distribution of the stars. — As the galaxy 
passes round the sky in nearly a great circle, the two points 
of the sky on either side, equidistant from that circle, may 
be called the galactic poles. Herschel I. made an elaborate 
investigation of the distribution of stars in the heavens by a 
system of "star-gauging." By counting the stars visible at 
once in the field of his telescope, and then comparing re- 
sults from different parts, of the sky, he found : 

That the spaces near the galactic poles contained the 
smallest average number of stars; 

That the average was generally the same at the same 
distance from the galactic poles ; 

That the averages increased with the distance, at first 
slowly, afterward much more rapidly; 

That in the galaxy, the stars were crowded so thickly as 
to defy counting. 

THEORIES OF THE GALAXY. 

578. Herschel's theory. — That the sun is a member 
of an immense system of stars which form a layer or bed 
of circular shape, having but little thickness in comparison 
with its breadth. That this bed is split near its southern 
edge, the two flat surfaces diverging as if a wedge had been 
driven between them. 

The figure shows a section of this supposed star-system, 
the sun being at S, not far from the split. 

Herschel supposed that the stars are distributed pretty 
uniformly throughout this space. If so, a telescope pointed 
toward B would include in a single field but few stars, be- 
cause the hue of sight would soon pass out oi the laver; if 
turned toward l\ more would be seen at once, and if toward 

I'\ a still larger number. Hence, he thought that his labors 
Ast.— 20. 



306 ELEMENTS OF ASTRONOMY. 

of star-gauging would show, approximately, the shape and 
size of the galaxy, and the place of the sun within it. 




579. This theory assumes two positions which are 
believed to be untenable. These are : 

1. That the stars are distributed uniformly. 

2. That instruments are made which can fathom the 
farthest depths of space, and will enable us to count all the 
stars which exist in the direction in which we look. 

But newer instruments of more delicate defining power 
continually reveal more stars, and Herschel himself finally 
admitted that the stars are greatly condensed in the imme- 
diate vicinity of the Milky Way. 

580. Madler's theory. — That the stars of the galaxy 
are arranged in an immense ring, or, perhaps, in several 
rings, one within another. To an observer within the sys- 
tem, the inner ring would seem to cover those beyond it. 

That the sun is within the system, but nearer to the 
southern side; for this reason, the southern portion is most 
brilliant. 

That the rings do not lie in the same plane; hence, the 
separation into two streams in the south, the divergence 
seeming necessarily greatest at the side nearest us. 

581. The dimensions of the galaxy are, of course, only 
a subject of speculation. From the magnitude of the stars, 
Herschel concludes that the remote parts are at least 2300. 



MOTION OF THE SOLAR SYSTEM. 307 

times the average distance of fixed stars of the 1st magni- 
tude. Light must occupy more than 10,000 years in coming 
from such a distance, or about 20,000 years in crossing from 
one side of this stellar system to the other. Herschel esti- 
mates the thickness of the stratum at about 80 times the 
distance of the nearest fixed star. 

582. Other galaxies, — Herschel and Madler agree that 
the sun is a member of this star-system. In the distant 
realms of space, this group of stars may present an appear- 
ance similar to that which we see in clusters already de- 
scribed. Herschel's scheme would indicate a planetary- 
nebula, Miidler's a ring-nebula. 

It may be then that the resolvable nebulae are other 
galaxies as large as our own, or even larger. How far away 
must the galaxy be removed from us that it may appear no 
larger than the ring-nebula in Lyra, which in Rosse's tele- 
scope seems less than an inch broad ? The distance is 
beyond imagination's utmost reach. We can only say that 
it is to ordinary stellar distances, as they are to the most 
trivial measurements on our earth. The light of such a 
cluster, so remote, must be more than a million of years in 
coming to the earth. 

Have we even then looked beyond the threshold of The 
Universe ? 

motion of the solar system. 

583. Proper motion of the stars. — Halley first con- 
ceived that even the fixed stars change their relative posi- 
tions. He found that the ancient places of Sirius, Ajrcturus, 
and Aldebaran did not coincide with positions which he 
himself had determined. James Cassini ascertained that 
Arc turns hail moved 5 minutes in [52 years, while neigh- 
boring stars had not been affected at all. 

By carefull) comparing and classifying all the proper 

motions then known, llersehel 1. was led to inter that the 



308 ELEMENTS OF ASTRONOMY. 

solar system was moving toward a point in the constellation 
Hercules, indicated by Rt. As. 17 h. 8 m., N. Dec. 25 ; 
shown by a small circle in Plate X. 

Other astronomers who have investigated this subject, 
agree in the general statement that the sun is moving towards 
a point in Hercules; as to the exact point they do not agree, 
but all place it in the small compass between R. A. 16 h. 
12 m. to 17 h. 7 m., and N. Dec. 14 26' to 39 54'. 

It has also been asserted that "the velocity of the motion 
is such that the sun, with the whole cortege of bodies depend- 
ing upon him, advances annually in the direction indicated, 
through a space equal to 1.623 radii of the terrestrial orbit," 
or 151 millions of miles. (W. Struve.) 

584. The orbit of this motion. — Continuing this in- 
vestigation, Madler concludes that the sun and all the mem- 
bers of the galactic system revolve about a center which he 
supposes to be Alcyone; the brightest star of the Pleiades. 
He estimates the sun's period of revolution to be 27 millions 
of years. 

The mutual attractions of so many heavenly bodies is likely 
to produce a motion of revolution, but the center of such 
motion must be sought in the plane of the galaxy. The 
Pleiades lie considerably to the south of that plane. Arge- 
lander suggests that such a center may be sought with more 
propriety in the constellation Perseus. 

Even if Alcyone were the center of the galactic system, it 
would by no means follow, as some have supposed, that that 
star is the center of the universe. The galactic system 
itself, can not be more than an individual member of a host 
of similar systems. 

THE MAGELLANIC CLOUDS. 

585. Near the south pole of the heavens are two 
masses of nebulous light which seem to be scattered frag- 
ments of the galaxy. Early voyagers in southern seas called 



RE CAPITULA TION. 309 

them "the Cape Clouds." Afterward they were named for 
Magellan, though by no right of discovery. They are known 
as the Great and the Small Cloud — Nubecula Major and 
Minor. The great cloud covers about 40 square degrees; 
the small is about one fourth as large. The region near 
the clouds is very poor in stars. 

586. In the telescope, a structure is revealed which 
includes the Magellanic clouds among the wonders of the 
heavens. They contain a great number of single stars, from 
the 5th to the nth magnitudes; very many star-clusters, 
irregular, oval, and globular ; and, finally, nebulae, separate, 
and grouped by twos and threes. In the great cloud are 
counted 580 single stars, 291 nebulae, and 46 clusters. 

These clouds seem to be miniatures of the celestial sphere, 
containing constellations, clusters of stars, and nebulous 
matter in different stages of condensation. 



587. RECAPITULATION. 

Fixed stars are classed in about 20 magnitudes ; the first six, includ- 
ing about 6000 stars, are visible to the naked eye. 

They are grouped in constellations ; the stars in each are numbered 
according to relative brightness. 

Stars are self luminous, therefore suns; the spectroscope indicates 
that among their many elements are some identical with those found 
in our sun, and in the earth, Many far surpass our sun in magnitude 
and brilliancy. 

The annual parallax of the fixed stars is very small, and for most 
is imperceptible ; hence, they must he very remote. Light COmes from 
the nearest in not less than 3.6 years; from some, in not less than 
8000 years. 

Stars vary in brightness. Some have faded, others have 
some have grown more brilliant, others increase and diminish with 

periodic regularity, They vary much in color, and sometimes 

color. 

Stars are double, treble, and multiple. Optically double stars, though 
very far apart, are so nearly in the Same line with the earth, that the 
light ol~ one is merged in that o( the other. 



310 ELEMENTS OF ASTRONOMY. 

Physically double or multiple stars show by rotation that some physical 
connection binds their components into a system. Some companion- 
stars have made an entire revolution about their primaries since they 
were discovered. The dimensions of orbits and masses of primaries have 
been computed. 

Many stars are grouped in clusters, probably by some physical 
connection. 

All nebulce were thought to be resolvable into star-clusters ; the spec- 
troscope indicates that many are irresolvable — mere cloudy, gaseous 
masses. They present various shapes — globular, elliptical, annular, 
spiral — and they are often exceedingly irregular. Often one or more 
nuclei are seen. Some are double, and multiple. 

The galaxy is a broad irregular belt of white light, which traverses 
the sky in nearly a great circle, and which is resolved by the telescope 
into an innumerable multitude of stars. Herschel believes that it is a 
great stellar system, of which the sun is a member ; that it is disposed 
in a lens-shaped mass, the stars being distributed throughout with con- 
siderable uniformity. Madler thinks the stars are arranged in one or 
more rings, not quite concentric. 

Many fixed stars have a small pi'oper motion; hence it appears 
that the solar system is moving through space. The motion is toward 
a point in the group Hercules, and is probably about a very remote 
center not yet known. Its rate is about 150 millions of miles per 
annum. 

The Magellanic clouds, bright patches near the south pole of the 
sky, are resolved into single stars, clusters, and nebulce, — entire stellar 
systems. 



CHAPTER XXIII. 



THE NEBULAR HYPOTHESIS. 



588. Evidences of law in the harmonies of the 
solar system. — A general review of the bodies which 
compose the solar system, and of their varied movements, 
shows a remarkable agreement in many important items. 
Such coincidences can not spring from chance, but must 
result from the wise plans of the Great Architect who laid 
the foundations of the universe, and placed thereon the 
infinitely glorious systems of worlds, of which ours is an 
example. Nor can we think that God creates as men build, 
laboriously adding part to part, making one thing and fitting 
another thereto, until the whole is finished. Probably a 
single planet added to, or taken from, the solar system would 
so disturb the equal balance of forces which hold the others 
in their places as to entirely derange, if not to utterly destroy, 
the whole. 

Wherever we question nature, we find that each oi her 
varied processes, the simplest or the most involved, proceeds 
by virtue of some law, which secures a degree of uniformity 
in results, while the influence o( peculiar circumstances, 
acting also in obedience to law, produces infinite variety 

within the limits of uniformity. We come to recognize 
among the sublimest attributes of Deity the wisdom which 
could devise, and the power which can enforce, laws which. 

by and through apparent confusion ami conflict, develop out 



312 ELEMENTS OF ASTR ONOM Y. 

of inert matter the wonderful mechanism of the Solar 
System and of the Stellar Universe. 

589. The harmonies of the solar system. — Among 
them we mention: 

1. All the planets, to the number of more than 200, 
revolve about the sun from west to east,* in orbits whose 
planes are nearly coincident with the plane of the sun's 
equator. 

2. The sun rotates from west to east. 

3. All the primary planets, so far as known, rotate from 
west to east. 

4. The satellites, so far as known, revolve about their 
primaries in the direction of the planet's rotation. Except 
the satellites of Uranus and Neptune, they revolve from 
west to east. 

5. The orbits of both planets and satellites have but slight 
eccentricity. 

6. The densities of the planets increase in nearly the 
order of their approach to the sun. This is also true, so far 
as known, of the relative densities of satellites about their 
primaries. 

590. The lessons of geology. — Geology teaches that 
the earth is probably a mass of molten material covered 
with a rigid, rocky crust but few miles thick. It teaches, 
farther, that the entire substance of the earth, including those 
elements which are melted with the greatest difficulty, was 
once fused. The heat which produced such fusion must 
have changed many substances, as water, compounds with 
carbon, and most metals, to the condition of vapor or gas. 
The appearance of the moon indicates that its nature is in 
this respect precisely like that of the earth; analogy leads 
us to suppose that all the planets and satellites are similarly 
constituted. 



*That is, toward the left, the observer being at the center of motion. 



THE HYPO THESIS ST A TED. 3 1 3 

If we may conceive a degree of heat sufficient to fuse a 
part, and to vaporize the rest of the substances which com- 
pose the earth and the planets, there is nothing to forbid the 
conception of a degree of heat sufficient to change every 
known or supposed substance to a gaseous form. 

591. Heat and motion are different manifesta- 
tions of the same force. — The investigations of Rumford, 
Joule, Tyndall, and others, show: 

1. That heat and motion, one force in two phases, are, 
like matter, indestructible. 

2. That heat may be converted into motion and motion 
into heat. 

The heat abstracted from the steam of the locomotive re- 
appears in the motion of the train. The motion of the 
cannon-ball, stopped by the iron armor of a ship, re-appears 
in the intense heat, both of the ball and of the plate struck — 
an amount of combined heat and force which has welded 
together two plates of the armor, at the place of the blow. 
The motion destroyed by friction explodes gunpowder, ignites 
wood, boils water, heats a rubbing axle red-hot. 

Professor Tyndall asserts that if the earth were instantly 
stopped in its revolution about the sun, the quantity of motion 
which the globe possesses being transformed into heat is 
sufficient to flash at once all the material of the earth back to 
its original state of vapor. " Behold the heavens shall be 
rolled together as a scroll, and the elements shall melt with 
fervent heat." 

THE HYPOTHESIS STATED. 

592. The nebular hypothesis supposes that a portion 
of space now occupied by the solar system, and extending 

far beyond the remotest planet, was filled originally with 

matter so intensely heated as to be in a vaporous or nebulous 
condition. The attraction o( gravitation between the par- 
ticles, and the various tonus o\ molecular attraction, though 



314 ELEMENTS OF ASTRONOMY. 

existing, would be neutralized, in the main, by the active 
repulsion of the intense heat. Some heat would radiate from 
the surface of the nebulous mass into the spaces beyond. 
The cooling material would begin to contract upon its center, 
under the action of gravitation, and, as is the observed action 
of matter when moving toward a center, would begin to 
rotate. But the motion produced would be at the expense 
of more heat, which would cause more contraction and more 
rapid rotation. The equatorial portion would finally acquire 
motion enough to counteract, as a tangential force, the attrac- 
tion of the central mass, acting as a radial force, and it would 
be left behind by the contracting center, forming a ring or 
zone. The same process repeated would throw of! one zone 
after another, each being denser than the preceding, until the 
glowing central sun would remain, about which all these, its 
offspring, revolve. 

As each zone was thrown off, or, rather, left behind, it 
must continue its motion of revolution about the central mass. 
The mutual attractions of the particles would cause them 
ultimately to unite in a spherical gaseous body, rotating upon 
its axis, and, by the same process which produced it, throw- 
ing off equatorial zones which become its satellites, revolving 
about it, as it revolves about the sun, and rotating upon their 
own axes. 

593. Peculiar results. — The rings of Saturn appear to 
have retained the ring form, condensed laterally into their 
present very thin shape. The group of minor planets be- 
tween Mars and Jupiter may be a ring which condensed 
about many nuclei, instead of one, none becoming powerful 
enough to absorb all the others. Leverrier has suggested 
the existence of a similar ring within the orbit of Mercury. 

594. The theory extended. — The same process may 
have produced like results in other realms of the universe. 
The condensing globe of nebulous matter may have con- 
centrated about two or more centers of internal attraction, 



ANOMALIES EXPLAINED. 315 

and thus systems of binary, ternary, or multiple suns may 
have been formed. Under such circumstances, these central 
masses must, as we know they do, revolve about their com- 
mon center of gravity. One nebulous mass may have another 
bound to it by the universal law of mutual gravitation. 



ANOMALIES EXPLAINED. 

595/ Retrogradation. — When the parts of the condens- 
ing ring came together to form a planet, while this planet 
must retain the motion of revolution, impressed upon it as 
a motion of rotation when it was a part of the sun, the mo- 
tion of rotation upon its own axis comes from the action 
of forces within itself, and may have gone to the right rather 
than to the left. But the motion of its satellites must con- 
form to its rotation. Hence, the retrograde motions of the 
satellites of Uranus and of Neptune offer no argument 
against the theory, unless it shall be found that the planets 
themselves rotate toward the left. 

596. Comets and meteorites. — In this concentration 
of the matter of the universe about centers, many portions 
would be left in the spaces between the spheres of contrac- 
tion, and would be joined to none. Such a portion would 
remain by itself, undergoing, doubtless, like action, until 
some solar system in its motion through space should come 
into its vicinity, bringing it within the influence of the new 
attraction. These isolated masses would join the larger 
systems as comets, or as streams of meteoric substances. 
Some comets may have come from fragments of nebulous 
rings, portions which did not coalesce with the rest, but were 
drawn aside by the attraction o\ the central mass, or o( other 
masses already condensed beyond them. 

597. Plateau's experiment. A mass o( oil is sus- 
pended in alcohol, diluted to exactly the density o( the oil; 



316 ELEMENTS OF ASTRONOMY. 

it readily arranges itself about a central wire, which may 
rotate as an axis, carrying the oil with it. 

The oil, being freed from the action of gravitation, assumes 
the form of a perfect sphere. 

When made to rotate, this globe becomes flattened at the 
poles; under more rapid rotation, the globe becomes a ring 
in the equatorial plane, which separates into small masses 
that at once assume globular forms, and often take, at the 
instant of formation, a motion of rotation on their own axes, 
usually in the direction of the rotating ring. 

A ring is sometimes formed while part of the original 
globe remains on the axis. 

Here we have most of the phenomena supposed by the 
nebular hypothesis, reproduced on a small scale. 

598. The nebulae. — To the hypothesis, it has been 
strongly objected that, if systems are developed in this 
manner, we might expect to find examples in all stages of 
progress among the innumerable objects in the sky; and 
that the facts of astronomy do not warrant the conclusions, 
under the assumption that all nebulae are resolvable by 
sufficient instrumental power. But some nebulae have never 
been resolved, and the spectroscope indicates that some 
are composed of gaseous matte}' alone. Some of the best 
known have changed both in form and brightness. The 
forms of globular, annular, spiral, and irregular nebulae at 
once suggest themselves as giving color to the hypothesis. 

599. The nebular hypothesis was advanced by Herschel 
I. in 1783, and was elaborately discussed by La Place. It 
has been the field of much astronomical, geological, and 
religious controversy. After each apparent defeat, it seems 
to have gained fresh vigor from new discoveries, and it is 
now very generally received by scientific men. 

Yet it remains but a theory, to give place instantly to any 
other which shall more completely or more simply explain 
all the phenomena of the universe. 



CHAPTER XXIV. 

THE CONSTELLATIONS. 

600. Celestial globes and star maps are often cov- 
ered with figures of men, animals, and monsters — imaginary 
forms which have descended from the ancient mythology 
and astrology. In a few cases, a fanciful resemblance may 
be traced; in most, the outlines of the map confuse the 
learner, because he can find nothing of the sort in the sky. 
''The constellations seem to have been almost purposely 
named and delineated to cause as much confusion and incon- 
venience as possible. Innumerable snakes twine through 
long and contorted areas of the heavens, where no memory 
can follow them ; bears, lions, and fishes, large and small, 
northern and southern, confuse all nomenclature."* 

In our star maps, the monsters are, therefore, omitted, 
and the sky is divided into districts, most of which retain 
their classical names. The learner will most easily find 
them by studying the simple geometrical figures which are 
formed by prominent stars. 

601. The Maps. — The circumpolar map, Plate VI., rep- 
resents so much of the sky as is included within the circle o( 
perpetual apparition for an observer at 40 N. l.at. The 
horizon lines are indicated, for eight months o\ the year, at S 
o'clock, p. m. ; by turning the map. it is easily rectified for 
any other hour or month. When studying it. the learner 
should face the north. 



J. F. W. Herschel, 

(317) 



318 ELEMENTS OF ASTRONOMY. 

Each of the equatorial maps, Plates VII.— XII. , shows the 
positions of the stars which are within 30 of the meridian 
at the time specified, and which lie between the horizon and 
the circle of perpetual apparition. This space is ioo° from 
south to north, and, therefore, extends io° beyond the zenith; 
it is 60 °, or 4 hours, wide; the six maps complete the circuit 
of the sky. 

602. To use the maps. — The learner should find the 
place of his meridian, and be able to trace it readily from 
south to north. The zenith found, it will not be difficult to 
fix a point on the meridian, 50 above the horizon, as the 
intersection of the equinoctial, and to trace the equinoctial to 
the east and west points of the horizon. These lines form 
the foundation of the work, and are represented by the 
vertical and horizontal lines which cross the center of the 
map. Face the south, and raise the map until the equinoc- 
tial line is opposite the equinoctial in the sky; the constella- 
tions will be found in their places on the day and hour 
mentioned. 

Nothing will supply the place of a few hours' work in the 
open air, month by month, as the seasons pass. A little 
patience with the maps, — alone, or with help from another 
who knows the stars, — will make any person thoroughly 
familiar with the sky. 

Two who study together will get much help from a very 
simple contrivance. Two light, straight rods are placed 
exactly parallel, and fastened to two cross-bars; while the 
teacher looks along one rod, which he points to any partic- 
ular star, the pupil looking along the other rod will readily 
identify the star. 

January 20, 8 p. m. 

603. The circumpolar map. Plate VI. — The most 
notable constellation is Ursa Major, the Great Bear. The 
seven bright stars of this group, east of the meridian, are 



THE CONSTELLATIONS. 319 

familiarly known as the great dipper. The pair of stars which 
form the upper side of the dipper, or that farthest from the 
handle, are called the pointers, because a line drawn through 
them passes very near the pole star. They are 5 apart, and 
hence are convenient to measure distances by. The star at 
the bend of the handle is Mizar; near it is a small star, 
Alcor, which has been considered a test of keen vision ; the 
Arabs called it Saidak, or the proof (541). 

Guided by the pointers, we easily find Polaris, a star of the 
2d mag. ; no star of equal magnitude is nearer to it than the 
pointers. From Polaris a line of small stars curves down- 
ward to the right and meets the upper of a pair of stars of 
3d mag.; with a faint star at the lower corner, these form 
a second or little dipper. The group is Ursa Minor. 

Draco nearly surrounds Ursa Minor. The head is at 
two bright stars near the horizon, about 15 west of the 
meridian; the body coils through the space between the 
two Bears. 

From Mizar draw a line through Polaris; at about the 
same distance on the opposite side are five rather bright 
stars, which form a rude, flattened letter M. They are the 
principal stars of Cassiopeia. Between Cassiopeia and Draco 
is Cepheus, while the large space void of bright stars on the 
opposite side of the pole is occupied by the Camelopard and 
the Lynx. 

604. The equatorial map. Plate VII.— Plate XI. is 
on the west; Plate VIII. on the east. Iannis is in the center 
of the field, just north of the equinoctial. West o\ the me- 
ridian is the beautiful cluster of the Pleiades; six may be 
counted on a clear night, the brightest being Alcyone, oi the 
3d mag. (584). East of the meridian and a little lower in 
altitude are the /lyades. often called the great A : at present, 
the stars are rather in the position o( a / '. Aklcluran. a 
red star of the 1st mag., forms one foot oi the letter; it is 
also the bulls eye. 



320 ELEMENTS OF ASTRONOMY. 

South-east from Taurus is Orion, the most beautiful group 
in our sky, and one of the few in which the outline of a man 
may be traced. Just south of the equinoctial, three stars of 
the 3d mag. form an oblique line, 3 in length. They are 
the girdle; a small star which marks a right angle with the 
lower end of the girdle is in the sword. Above, two bright 
stars, Betelgeuze the eastern and Bellatrix the western, form 
the shoulders, while a small triangle of three stars marks the 
head. Below the girdle, Rigel, of 1st mag., marks the right 
foot; a smaller star, east of Rigel and opposite Bellatrix, 
shows the left knee, on which the man is kneeling as he 
fights the bull. 

A small triangle below Rigel, and a trapezoid south of the 
girdle, mark the constellation Lepus. 

West of the Pleiades, the single bright star is Alpha Arietis, 
or simply Arietis; it marks the Tropic of Cancer and the 
second hour-circle. South of Arietis and west of the girdle 
of Orion is the star Mira (547), in the constellation Cetus. 
Mira and the girdle are about equally distant from the 
Pleiades, and the three form a right angle at the Pleiades. 
Another bright star of Cetus lies in a line between Mira 
and Aldebaran. 

The space south of Taurus, between Orion and Lepus on 
the east and Cetus on the west, is occupied by Eridanus, 
with few notable stars. 

North of Aldebaran and near the zenith is the beautiful 
blue star Capella, of the 1st mag., in Auriga ; it is attended 
by a star of 2d mag., about 5 to the east. Midway between 
Capella and Bellatrix, a bright star is referred indifferently to 
Auriga or to Taurus. 

Perseus lies west of Auriga, its brightest star, Alpha Persei, 
being nearly due west of Capella, and but little nearer the 
zenith; a line from Rigel through Aldebaran meets this star. 
Algol (546) is south-west from Alpha Persei, nearly in a line 
with Arietis, which is equally distant from Algol and the 
Pleiades. 



THE CONSTELLATIONS. 321 

605. In the east. — A line from Aldebaran through Bella- 
trix meets, in the south-east, Sirius, the brightest star of the 
sky. Farther toward the east, Procyon makes an equilateral 
triangle with Sirius and Betelgeuze. Near the prime vertical 
and about midway to the zenith are the two bright stars, 
Castor and Pollux, while farther toward the north Regulus 
and the sickle are just visible in the haze above the eastern 
horizon. 

606. In the west. — Four large stars form a nearly square 
figure whose diagonal is near the prime vertical; the largest 
is Alpheratz of Andromeda. The square is the square of 
Pegasus.' Two prominent stars between Alpheratz and the 
zenith, with Algol and the square, form a figure much like 
the great dipper, but larger; the handle may end with Algol 
or with Alpha Persei. 

In the north-west, Deneb of Cygnus is just setting. 

The galaxy crosses the sky in a great circle from north- 
west to south-east, passing Deneb, Cassiopeia, Perseus, and 
between Taurus, Orion, and Sirius on the one side, and 
Capella and Procyon on the other. 

March 21, 8 p. m. 

607. The equatorial map. Plate VIII. — The central 
star of the map is Procyon of Cants Minor; it is about 5 
west of the meridian and north of the equinoctial. North 
of Canis Minor, the zodiacal constellation Gemini is marked 
by the two bright stars Castor and Pollux, Castor being the 
highest and brightest. Gemini meets Taurus and Orion 
near the western margin of the map. ami Cancer at the 
meridian. Cancer contains no bright stars, but about equally 
distant from Procyon, Castor, and Regulus is a remarkable 
cluster o( stars, called Prasepe (501), the manger, and some- 
times the Beehive. 

This map has been extended a little toward the east in 

order that it may include Regulus. the brightest star o\ 

Am.— ai. 



322 ELEMENTS OF ASTRONOMY. 

which lies on the ecliptic and very near the tenth hour- 
circle. In this constellation, six stars form the rude outline 
of a sickle, Regulus being at the end of the handle; they 
also show the head of the Lion, Regulus being the heart. 

South-west from Procyon is the beautiful constellation 
Cams Major, studded with bright stars. Sirius, with a star 
about 5 ° west of it, and two others about equally distant from 
each other, but farther south, form an oblique parallelogram, 
inclined toward Orion. 

The space between the two Dogs, Gemini and Orion, is 
occupied by Monoceros. East of Monoceros, and south of 
Cancer, is a part of Hydra, whose only bright star is Cor 
Hydrae, south of Regulus. Argo is in the south, near the 
horizon. 

608. In the east. — Arcturus, the bright star of Bootes, 
has just risen; a line which joins it with Polaris passes 
between the last two stars in the handle of the Dipper. 
Denebola, in Leo, is nearly in a line which joins Arcturus 
and Regulus. 

In the west. — Capella has passed to the north of the 
prime vertical, and is about 30 ° from the zenith. The 
Pleiades are midway between Capella and the horizon. 
Orion, Aldebaran, and Sirius are bright in the south-west. 
Arietis is near the horizon in the north-west; Algol is in the 
great arc of bright stars which begins at Arietis, sweeps 
through Capella and its comrade, Castor and Pollux, and 
ends with Procyon or Sirius. 

The galaxy may be traced in a great circle from the north 
to the south, crossing the prime vertical in the west about 
50 above the horizon. 

May 21, 8 p. m. 

609. The equatorial map. Plate IX. — Leo, the 
brightest constellation, has just passed the meridian, and 



THE CONSTELLATIONS. 323 

occupies the western central part of the map; Denebola, the 
most eastern star of the group, is about 30 from the zenith, 
and very near the meridian. Two smaller stars to the west- 
ward of Denebola form a right-angled triangle with it. 
Regulus marks the ecliptic and the tenth hour-circle. 

South-east from Leo, and on either side of both equinoctial 
and ecliptic, stretches the constellation Virgo. Its brightest 
star, Spica, of 1st mag., is very near the ecliptic; it forms a 
large equilateral triangle with Denebola and Arcturus. 

South-west from Spica, and nearly on the meridian, four 
stars of medium brightness, in a trapezium, mark the Crow ; 
Crater is west of the Crow, and south of Leo ; south of Virgo, 
Corvus, Crater, and Leo, sweeps the long trail of Hydra, 
whose only bright star, Cor Hydrae, is south-west of Regulus. 

Between Leo and the Bear a few small stars mark the place 
of Leo Minor. A cluster of stars called Berenice's Hair lies 
west of Arcturus and north-east of Denebola. Canes Venatici 
occupy the remaining space to the Dipper; the principal star 
is Cor Caroli, of 3d mag. 

610. In the east. — Arcturus is most prominent directly 
south-east from the Bear. Arcturus and Spica form the base 
of a large isosceles triangle, whose vertex is in a bright star 
of Scorpio, just risen in the south-east. Below the head of 
Draco, Vega, the bright star of Lyra, is well up in the north- 
east. Between Vega and Arcturus glistens the circlet of the 
Northern Crown, on the prime vertical, about halfway to the 
zenith. A little south of east, the long line of stars which 
forms the Serpen t stands perpendicular to the horizon. 

In the west. — The Twins are midway between the Hip- 
per and the horizon] in the north-west, Capella ami iis mate 
have about the same altitude. South-west from the Twins, 
Procyon is nearly set. 

The galaxy lies in a great circle just above the horizon, 
from the west through the north to the east; it is usually 
invisible, because of the haze. 



324 ELEMENTS OF ASTRONOMY. 



July 22, 8 p. m. 

611. The equatorial map. Plate X. — The brightest 
constellation is Scorpio, midway between the equinoctial and 
the horizon. Its largest star, Antares, of 1st mag., is about 
5 east of the meridian; on the meridian is a star of 2d mag., 
and two others of 3d mag. are a little lower, to the west; the 
four form a figure like a boy's kite, to which a line of stars 
below Antares forms the tail. The Tropic of Capricorn and 
the ecliptic pass through the kite above Antares. 

Between Scorpio and Virgo is Lib7'a, shown by two stars 
of 3d mag., which mark the scales; they are about equally 
distant from a line which joins Antares and Spica. 

North-east of Scorpio is Ophiuchus, covering a space, not 
well supplied with bright stars, more than 40 ° in width; two 
stars of 3d mag., about io° apart, lie east of Antares; Alpha 
Ophiuchi is nearly on the line from Antares to Vega, and 
12 north of the equinoctial. 

The center of the map is occupied by the Head of Serpens, 
the brightest star being about 7 north of the equinoctial 
and west of the meridian. Two stars below and three above 
form an outline like the crook of a shepherd's staff. 

North of Serpens is the Northern Crown, a semicircle of six 
stars; the central and brightest is called the Gem. 

West of Serpens and the Crown is Bootes, extending from 
Virgo to Draco. The principal star is Arcturus, a red star 
of 1st mag., about 30 from the zenith in the south-west. 
Four stars west of the Crown form a cross; with Arcturus 
and two to the south-east, an irregular figure 8. 

East of Serpens and Corona, Hercules occupies the space 
between Ophiuchus and Draco. The brightest star, of 2d 
mag. , lies between the Gem of Corona and Alpha Ophiuchi ; 
it forms an isoscles triangle with the Gem and the bright star 
of the Serpent. A flattened arc of small stars extends 
from this star beyond the zenith. The small circle on the 



THE CONSTELLATIONS. 325 

map marks the point toward which the solar system is 
moving (583). 

612. In the east. — Vega is east of the zenith. Farther 
north, in the Milky Way, about 45 ° from the horizon, is 
Deneb, the chief star of Cygnus. South-east, and also in 
the galaxy, is Altair, of the Eagle, easily recognized by its 
two bright attendants in a vertical line. Near the horizon, 
the bright stars of Pegasus appear in the north-east. 

In the west. — Spica is low in the south-west, and Reg- 
ulus is near the western horizon. 

The galaxy passes from north to south, crossing the prime 
vertical about midway to the zenith. 

September 23, 8 p. m. 

613. The equatorial map. Plate XI. — The central 
figure is Aquila; its brightest star, Altair, of 1st mag., being 
west of the meridian and north of the equinoctial ; a star of 
3d mag. is near it on either side; the line of the three pro- 
longed meets Vega west of the zenith. 

Sagittarius lies south of Aquila; four small stars in a 
trapezoid, with another to the west, form what is sometimes 
called the "milk dipper;" the handle has fallen into the 
Milky Way. 

Capricornus is east of Sagittarius and south-east of Aquila ; 
two small stars near the meridian are the only ones of note. 
North-east of Capricornus is Aquarius. 

North-east of Altair, four small stars in a trapezoid mark 
the Dolphin. 

In the zenith we find Cygnus; its brightest star is Deneb, 
of 1st mag., in the body of the bird. The head is at a star 
of 2d mag., almost in line with Vega and Altair; four stars 
of 3d mag., which form a line across the body between the 
head and Deneb, mark the wings. 

Lyra occupies the space between Cygnus and Hercules. 
Vega is the bright star nearest the zenith. 



326 ELEMENTS OF ASTRONOMY. 

614. In the east. — The great square of Pegasus is on the 
prime vertical, midway to the zenith. Arietis and Algol have 
risen in the north-east; Capella is peering through the mists 
still farther north. 

In the west. — Arcturus hastens to his setting; the Crown 
is on the prime vertical; the Serpent is south-west of the 
Crown, and south of Arcturus. 

The galaxy crosses from north-east to south-west through 
the zenith. 

November 22, 8 p. m. 

615. The equinoctial map. Plate XII. — The central 
figure is the square of Pegasus, the eastern side being on the 
meridian. Although called the square of Pegasus, the 
brightest star is Alpheratz, of Andromeda. Two stars to the 
north-east, in line with Alpheratz, also belong to Andromeda. 

East of Pegasus is the constellation Pisces, of the zodiac, 
without any notable stars. Directly south of Alpheratz and 
its companion in the square is the Vernal Equinox. 

Aquarius lies south-west of Pisces and Pegasus ; its bright- 
est stars are a pair of 3d mag., near the equinoctial, on the 
western side of the map. 

South of Aquarius and near the horizon, we find a star of 
1 st mag., Fomalhaut, of Piscis Australis. 

East of Aquarius and south of Pisces is Cetus ; a star of 
2d mag., about io° east of the meridian, marks the tail of 
the monster ; farther east, five stars make a rude sickle in the 
body; still farther east, two stars of 2d mag., one of which is 
Mira, form the head. 

616. In the east. — Orion's belt appears at the horizon, 
preceded by Betelgeuze and Bellatrix, and followed soon by 
Rigel. The Pleiades are midway to the zenith ; Aldebaran 
is between the Pleiades and the Girdle. Perseus lies between 
the Pleiades and the zenith. In the north-east, Capella and 



THE CONSTELLATTONS. 327 

its comrade are about 30 above the horizon; and below 
them, just rising, are the Twins. 

In the west. — Cygnus is on the prime vertical, opposite 
Perseus ; Aquila with Altair is south of west, about 20 from 
the horizon. 

The galaxy crosses from west to east through the zenith. 

No season of the year gives at this hour of the night a 
finer display of stars. Except Canis Major, Scorpio, and 
Leo, all the brightest constellations which ever appear above 
our horizon are visible, with the largest proportion of bright 
stars. 



APPENDIX 




I. The meridian altitude of the equinoctial = the 
co-latitude of the observer (51). Let HPO be the 

visible half of the observer's meridian; P, the pole; E, the 

intersection of the meridian and 
the equinoctial; EO equals the 
meridian altitude of the equindt- 
tial; PH, the latitude of the 
observer (39). From the semi- 
circumference MZO, take the 
quadrant PE; the remaining arcs, 
PH and EO, are together equal 

to a quadrant; hence, either of them is the complement of 

the other (Geom. 207, 94). 

II. The sextant (115). When the index-arm AO is at 
zero, at JV, the index-mirror 
A is parallel to the horizon- 
glass B. Let the index- 
arm be so moved that a 
ray from the star S is 
reflected to the horizon- 
glass, and thence to the 
eye at K, in coincidence 
with a ray UK from a 
second object. The angle 
OAJV, traversed by the 
index-arm, is half the an- 
gle SCH, between the two bodies. 

(328) 




Fig. 175. 



APPENDIX. 



3 2 9 



(Art 72) SAI = 

LBA = 

(Geom. 261) SCH = 

iSo° — 2BAO- 

(Geom. 125) LBA = 

.-. y 2 SCH: 



2BAO; 



D. 




^0 . '. SAB = 180 — 2BAO; 
L'BC.-. ABC= iSo° — 2ZBA; 
SAB — ABC = 
~{i8o° — 2LBA) = 2LBA 
BAN. 
= BAN — BAO = OAN, Q. E. 

III. The sun's declination (131) may be sought in the 
nautical almanac, or is found as follows : 

In the spherical triangle ABC, right-angled at C, let A 
be the vernal equinox, and B the 
place of the sun. AB, part of 
the ecliptic, is the sun's longitude 
(119); AC, part of the equinoctial, 
Flg - I76, is the sun's right ascension (35); 

BC is the declination required. A is the obliquity of the 
ecliptic, 23 ° 27' 14" (58). The sun's longitude may be com- 
puted from his motion, or may be observed with the transit 
and clock. Then (Geom. 882), 

sin C : sin A : : sin AB : sin BC. 

IV. The radius vector describes equal areas in 
equal times (204). In Fig. 69, take the first two sections 
from A to G, and draw FO. The 

triangles AOD and DOB have equal 
bases, AD and DF, and their vertices 
are at the same point, O; hence (Geom. 
388), they are equivalent. The tri- 
angles DOF and DOG have the 
common base DO, and their vertices 
are in the line FGr } parallel to the 
base; hence, they are equivalent. 
That is, 



AOD=DOF^~ DOG. 
Similarly, 
AOD DOG =GOK A'O.V V(>A\ 




Fig. 177. 



etc. (Fig. 09.) 



33° 



ELEMENTS OF ASTRONOMY. 



V. The precession of the equinoxes (229). The 
equatorial radius is longer than the polar radius by about 13 
miles (154). We may consider that the earth is a sphere 
surrounded by a belt of matter which is 13 miles thick at the 
equator, and diminishes to nothing at the pole. We may 
call it the equatorial belt. The precession of the equinoxes is 
caused by the unequal attraction of the sun and moon upon 
different parts of this belt. 



** 




Fig. 178. 



Let abed represent the earth's equator, and axcy the plane 
of the ecliptic. Let us consider the effect of the sun's 
attraction upon two particles, b and d, at opposite sides of 
this belt ; the diameter which joins them is equivalent to a 
rigid bar, or lever, whose fulcrum is at 0, the center of the 
earth. 

When the earth is at the equinoxes, the sun is in the 
direction of the line ac ; the particles b and d, are equally 
distant from the sun, and are, therefore, equally attracted. 

When the earth is at the solstice, the sun is in the line ox; 
b is nearer the sun than d, and is, therefore, more strongly 



APPENDIX. 331 

attracted; the tendency of the sun's force is to draw the bar 
bod into the line xoy. But the bar has with the earth a 
motion of rotation about in the plane abed; this force of 
rotation unmodified would keep it always in that plane, and 
the particle b would fall on c. The sun's attraction draws b 
a little aside from the path it would follow if influenced only 
by rotation, and it falls upon e', a little backward, or west- 
ward of e. While b, in its journey from a to e, has been thus 
drawn aside, d, at the other end of the bar, being attracted 
less strongly by the sun, has in like manner been forced out 
of the path which rotation alone would have marked for it, 
and it falls upon a', a little behind a. The result is that the 
diameter bod does not come back to the place aoe, but is 
twisted about into a new position a'oc' . What is true of the 
two particles b and d, is true of all other particles in the 
equatorial belt, since all in succession are similarly affected 
by the sun's attraction. Hence follows a constant westward 
motion of the line which joins the points where the ecliptic 
and the equator meet, or the equinoxes. 

As the particles in the equator ascend from a, the angler/ 
which they make with the ecliptic is diminished, while as 
they descend toward e their angle is increased ; the two 
effects counterbalance, leaving the angle between the two 
planes unchanged, but causing a slight rolling motion of one 
on the other. 

Thus for we have confined our thoughts to the influence 
of the sun's attraction upon the equatorial belt. But any 
external force which is out of the plane of that belt will have 
a similar effect. The influence of the moon is even greater 
than that of the sun in causing precession, because the moon 
is so much nearer the earth. 

As the equinoctial has this slow rolling motion upon the 
ecliptic, it is evident that the axis o\ the earth has a motion 
of revolution about the axis of the ecliptic. The pole of the 
heavens is moving about the ecliptic pole at a distance o( 
about 23 28'. The time o\ a complete revolution is found 



33 2 ELEMENTS OF ASTRONOMY. 

by dividing 360 by 50", the amount of annual precession; 
it is about 26,000 years. During that time the pole will 
move through the constellations Cepheus, the Swan, the 
Lyre, Hercules, and Draco, and will finally return to its 
present place. 

VI. Nutation. — The plane of the moon's orbit makes an 
angle of about 5 (358) with the ecliptic. The line of the 
nodes (359) revolves once in about 19 years, changing the 



Fig. 179. 

moon's extreme declination from 28^°, when its precessional 
effect is greatest, to i8^°, when that effect is least. Hence, 
the pole of the equinoctial is drawn from the pole of the 
ecliptic, alternately less and more than the average, and 
describes, not an exact circle, but a waved line, as in the 
diagram. This waved motion of the pole is called nutation. 
Its effect is to cause a slight displacement of the stars, alter- 
nately increasing and diminishing their declination. The 
effect of precession is to increase their right ascension 
regularly. 

VII. Ecliptic limits. Of latitude (373). Let S rep- 
resent the sun, E the earth; M the moon; SEA marks the 
plane of the ecliptic. Draw DA tangent to the surfaces of 
the sun and earth. It is evident that the surface of the 
moon must come within this line in order that an eclipse 
of either sun or moon may occur. HEM is the angular 
distance of the center of the moon from the ecliptic, or the 
limit of latitude, at which a solar eclipse may occur; I EN 
the limit of latitude of a lunar eclipse. 



APPENDIX. 333 

SED is the angle of the sun's apparent radius; 

BEM, or CEN, " moon's 

EDK " sun's horizontal parallax; 

EBK " moon's " 




Fig. 180. 



From the figure, HEM= SED + BEM + DEB. 
Because EBK is exterior to the triangle DBE, 
DEB=EBK— EDB (Geom., 261). 
Substituting, HEM= SED + BEM+ EBK— EDB. 

Translating : 7/fo Zw«? ^/" latitude for a solar eclipse equals 
the sum of the solar and lunar apparent radii, plus the differ- 
ence between the solar and lunar horizontal parallaxes. 

Omit the solar parallax, because it is very small, and 
substitute the largest possible values of the other quantities. 

ETEM=z \G%' -f 16^' +62'= 95'; if the moon's latitude 
at inferior conjunction be so much, an eclipse may occur. 
Again, 15^' -|- 14^'+ 53 }4' — 84': if the latitude be so 
much, an eclipse must occur. 

Again, from the figure, TEN CEN \ CEA. 
Because ECK is exterior to the triangle AC If 
CEA = ECK— EAC 

Because SE/) is exterior to the triangle If IP. 
EAC SED EDK, 

Substituting, first, CEA ECK— SED EDK 
Next, TEN CEN \ ECK SED \ EDK 



334 



ELEMENTS OF ASTRONOMY. 



Translating : The limit of latitude for a lunar eclipse equals 
the moon's apparent radius, minus the sun's apparent radius, 
plus the sum of the solar and lunar horizontal parallaxes. 

Applying values as before, i6^' — 15^' + 62' = 63', the 
limit when greatest; 14^' — 16^' -f- 53^2' = 52', the limit 
when least. 

VIII. Ecliptic limits. Of longitude. — From the 
limits in latitude those in longitude are readily found. In 
the right-angled triangle ABN, the angle iV^is the inclination 
of the moon's path to 

the ecliptic, therefore = 

5 9' (336); the side AB 

is the limit of latitude, 

as found above, and the 

side NB is required. 

The solar ecliptic limit 

is about 1 7 (15 20' to 

18 36'); the lunar ecliptic limit, about 12 (9 23' to 12 

24')- 

IX. Airy's experiment (171). Spheres of like density 
are to each other as the cubes of their radii (Geom. 806); 
spheres of unlike density are as the products of their respec- 
tive densities into the cubes of their radii. Hence (158), 




Fig. 181. 



G : G : : 



dR* d'R' 



Ri 



R"> 



dR : d'R' 



Even if R' is less than R, d! may be enough larger than d 
to make d'R' > dR, and, therefore, G' > G. 



TABLES 



TABLE [.-EQUATION OF TIME. 





5 


10 


15 


20 


25 


30 


January 


M. S. 

5 50 


M. S. 

7 56 


M. S. 

9 49 


M. S. 

11 25 


M. S. 

12 41 


M. S. 

13 37 


February 


14 16 


14 28 


14 20 


13 55 


13 12 


12 15 


March 


12 35 


10 21 


8 58 


7 30 


5 59 


4 26 


April 


2 38 


1 14 


4 


1 12 


2 10 


2 57 


May 


3 29 


3 48 


3 52 


3 41 


3 18 


2 43 


June 


i 46 


5o 


13 


1 18 


2 22 


3 22 


July 


4 18 


5 05 


5 41 


6 05 


6 14 


6 09 


August 


5 43 


5 05 


4 13 


3 08 


1 50 


23 


September 


I 32 


3 13 


4 58 


6 44 


8 28 


10 08 


October 


11 40 


13 03 


14 14 


15 11 


15 52 


16 15 


November 


16 17 


15 55 


15 12 


14 08 


12 45 


1 1 02 


December 


9 03 


6 51 


4 28 


2 01 


28 


2 55 



Full-faced, figures show thai the clock is fasierth&n the sun. 

Plain figures show that the clock is slower than the sun. 

The equation is given in minutes ami seconds tor each fifth day. 
It is found for intervening thus thus: Suppose the equation is sought 
for Feb. 12. The difference between the tabular numbers tor Feb, 
10 and 15 is (14 28 — 14 20) 8 seconds; | o\ 8 sec, is .; sec.j 
14 28 — 3 14 25, the equation sought. Observe the different 
treatment required tor, say, July S. or April 14. 

The table is for the year 1885; but will not differ materially foi 
several subsequent years. 



TABLE II. 



To find the day of the week on which the first day of any month 
falls, from 1753 to 1905. 



USE OF THE TABLE. 



In the table on the following page, look for any year ; below, in 
the same column, will be found the day of the week on which each 
month of that year begins. Thus, in the year 1753, 1759, 1770, etc., 
January begins on Monday, February on Thursday, March on Thurs- 
day, April on Sunday, etc. 

On leap years, marked by full-faced type, the months from March 
forward begin one day later than the day found in the table. Thus, 
1776 being leap-year, March 1 fell on Friday instead of on Thursday. 

Days of the month which fall on the same day of the week : 

1, 8, 15, 22, 29. 4, 11, 18, 25. 

2, 9, 16, 23, 30. 5, 12, 19, 26. 

3, 10, 17, 24, 31. 6, 13, 20, 27. 

7, 14, 21, 28. 

Example.— The battle of Waterloo was fought on the 18th of 
June, 1815. What was the day of the week? 

Solution. — The year 1815 is found in the last column, and is not 
leap-lear. The first of June fell on Thursday, as did also the 8th 
and 15th, and the 18th was Sunday. 

Example. — On what day of the week will Christmas fall in 1896? 

Solution. — 1896 will be leap-year, and is found in the third 
column. The 1st and the 22d fall on Tuesday and the 25th on 
Friday. 





D. 


H. 


M. 


s. 


Mean Solar Day, . 




24 






Sidereal Day, 




23 


56 


4.o< 


Mean Lunar Day, . 




24 


54 




Mean Sidereal Year, 


• 365 


6 


9 


9.6 


Mean Solar or Tropical Year, 


• 365 


5 


48 


46. 


Mean Anomalistic Year, 


• 365 


6 


13 


49-3 


(336) 

















TABLE II. 










1753 


1754 


1755 


1756 




1757 


1758 




1759 


60 




61 


1762 


63 


64 






65 


66 


67 


68 




69 




1770 


71 


72 




73 


74 


75 




1776 




77 


78 


79 


80 






1781 


82 


83 


84 




85 


86 




1787 


88 




89 


90 


91 


92 






93 


94 


95 


96 




97 




1798 


99 


1800 


1801 


1802 


1803 


1804 






1805 


6 


7 


8 




9 




1810 


11 


12 




13 


H 


15 




1816 




17 


18 


19 


20 






1821 


22 


23 


24 




25 


26 




1827 


28 




29 


30 


3i 


32 






33 


34 


35 


36 




37 




1838 


39 


40 




41 


42 


43 




1844 




45 


46 


47 


48 






1849 


5o 


5i 


52 




53 


54 




1855 


56 




57 


58 


59 


60 






61 


62 


63 


64 




65 




1866 


67 


68 




69 


70 


71 




1872 




73 


74 


75 


76 






1877 


78 


79 


80 




81 


82 




1883 


84 




85 


86 


87 


88 






89 


90 


9i 


92 




93 




1894 


95 


96 




97 


98 


99 




1900 


1901 


1902 


1903 


1904 




1905 


Jan. 


M. 


Tu. 


W. 


Th. 


F. 


Sa. 


Su. 


Feb. 


Th. 


F. 


Sa. 


Su. 


M. 


Tu. 


W. 


Mar. 


Th. 


F. 


Sa. 


Su. 


M. 


Tu. 


w. 


April 


Su. 


M. 


Tu. 


w. 


Tli. 


F. 


Sa. 


May 


Tu. 


W. 


Th. 


F. 


Sa. 


Su. 


M. 


June 


F. 


Sa. 


Su. 


M. 


Tu. 


W. 


Th. 


J^y 


Su. 


M. 


Tu. 


W. 


Th. 


F. 


Sa. 


Aug. 


W. 


Th. 


F. 


Sa. 


Su. 


M. 


Tu. 


Sept. 


Sa. 


Su. 


M. 


Tu. 


\V. 


I'h. 


F. 


Oct. 


M. 


Tu. 


W. 


Th. 


F. 


Sa. 


Su. 


Nov. 


Th. 


F. 


Sa. 


Su. 


M. 


Tu. 


\Y. 


Dec. 


Sa. 


Su. 


M. 


I'u. 


w. 


Th. 


F. 



337 



Ast.— 33. 



338 



ELEMENTS OF ASTRONOMY. 



> z z Q 



5 a z a 

h a 2 b 

s ° h 3 

s a o o 



« 5 J 

Ss<o 

Is 71 



VO VO On h tJ- 
ro in ro 



oo ro o vo 



r-~ vo m cm CM 












O 


CM 


on 


00 


CM 














i/i 






cj 




VO 


O 


OO 


OO 


















o\ 






>« 










" 


CM 










H 


VO 


o 


m 





H 











in 


fX) 


0() 






CM 


l/> 

>s 


Ov 


t-s 


N . 


o\ 


m 


ri 


oo 


r- 



N ■+ m VO 



"* o o o 



VO •*■ CM vo Os 



to vo vo co 



lO VO Ov 
O ro Os 
vo vo 







Ov On 
C-~ VO 



00 CM O 



CO VO Oi ■* 



VO H * 

ro vo" h" 



H 00 CM 

Oi a m co r^ 



m Ov ON 



Soo - 5 



■* Ov 00 Ov 



-*- c-« o vo ■<*• 



X»O+®<rO^„D>!S>0f 



J2 • u £ 3 



§>H§^D2 



G| 



H 


CM VO 
O OV M M 


8 8 

C X 
\r vo' 
CM CM 


O OO VO Q O 
oo • C oo 

"2 ti o ^ ^ 

ro -tf- in cm Ov 
ff° ro" M 



cm in ^-*" *"• 
rooo covo 



§2P 



. <u 

: c 2 c 

i C !3 1 



VO C 
CM O 



t~» H 




CO 


r>N in 


OV00 


ro 


co 


- 00 00 




tv 


t>» CO CM 


« 


- H 








"" 








ro 




CM 






8 




8 






ro 


OvVO 






< 


8 




m 


OvVO 


Ov CM 




























CM t»s 


C^ 


* 


'-: 




CM 


in 


vo 


CM 



3» -" • V f j 



TABLE IV.-THE MINOR PLANETS. 



NO. 


NAME. 


D 


SCOVERED. 


ORBIT. 


WHEN. 


BY WHOM. 


DIST. 


ECCEN. 


INCLIN. 


PERIOD. 










©=I. 




r 


Years. 


z 


Ceres. 


1801 


Piazzi. 


2.766 


.080 


10 36 


4.60 


2 


Pallas. 


1802 


Others. 


2.770 


.240 


34 42 


4.61 


3 


Juno. 


1804 


Harding. 


2.669 


.256 


*3 3 


436 


4 


Vesta. 


1807 


Olbers. 


2.360 


.090 


7 8 


3.63 


5 


Astrsea. 


1845 


Hencke. 


2.578 


.190 


5 19 


4.14 


6 


Hebe. 


1847 


Hencke. 


2.425 


.201 


14 46 


3-78 


7 


Iris. 




Hind. 


2.386 


.231 


5 27 


3-69 


8 


Flora. 




Hind. 


2.20I 


•157 


5 53 


3-27 


9 


Metis. 


1848 


Graham. 


2.386 


.123 


5 36 


3-69 


IO 


Hygeia. 


1849 


DeGasparis. 


3-149 


.lOI 


3 47 


5-59 


„ 


Parthenope. 


1850 


DeGasparis. 


2-453 


.099 


4 36 


3-84 


12 


Victoria. 




Hind. 


2-333 


.219 


8 23 


5-57 


J 3 


Egeria. 




DeGasparis. 


2.576 


.087 


16 32 


4-13 


14 


Irene. 


1851 


Hind. 


2.590 


.165 


9 7 


4-17 


15 


Eunomia. 




DeGasparis. 


2.643 


.188 


n 44 


4-3° 


16 


Psyche. 


1852 


DeGasparis. 


2.926 


.136 


3 4 


5-oi 


17 


Thetis. 




Luther. 


2.474 


.127 


5 35 


3.89 


18 


Melpomene. 




Hind. 


2.296 


.217 


10 9 


3-48 


x 9 


Fortuna. 




Hind. 


2.441 


.158 


1 32 


3.8a 


20 


Massilia. 




DeGasparis. 


2.409 


.144 


41 


3-74 


21 


Lutetia. 




Goldschmidt. 


2 -435 


.162 


3 5 


3-oS 


22 


Calliope. 




Hind. 


2.909 


.104 


13 44 


4.96 


2 3 


Thalia. 




Hind. 


2.625 




10 13 


4.26 


24 


Themis. 


1853 


DeGasparis. 


3142 


.117 


4 S 


5-57 


25 


Phocea. 




Chacornac. 


a, i>'.' 


•253 


ai 34 


.:•--■ 


26 


Proserpine. 




Luther. 


2.656 


.oSS 


3 33 


4-33 


27 


Euterpe. 




Hind. 


a-347 


•173 


1 35 


;.oo 


28 


Bellona. 


1854 


Luther. 


a.778 


.150 


9 21 


4.03 


29 


Amphitrite. 




M.u-th. 


2.555 


.072 


6 - 




30 


Urania. 




Hind. 


2.364 


.1 17 




3.63 


31 


Euphrosyne. 




Ferguson, 


3.X56 


.216 


36 25 


5-6i 


32 


Pomona. 




Goldschmidt. 




.089 


■ ' 


t.16 


33 


Polyhymnia. 




Chacornac. 


B.865 


.338 






34 


Circe. 


e8 


Chacornac. 


B.68I 


.llo 


5 -•' , 




35 


1 teucothea. 




Luther. 


3.000 


•M 


S 10 


• 


36 


Aialanta. 




Goldschmidt. 


• 749 




18 i- 




37 


Fides. 




Luther. 




I7S 




4 JO 


38 


Leda, 


185(6 


Chacornac. 


■ M« 




6 58 


4 54 


39 


1 itetitia. 




Chacornac. 


2.771 


.111 


10 - - i 


4-W 


40 


1 [armonia, 




Goldschmidt. 




,046 


1 1 j 





34Q 



ELEMENTS OF ASTRONOMY. 



NO. 


NAME. 


DISCOVERED. 


ORBIT. 


















WHEN. 


BY WHOM. 


DIST. 


ECCEN. 


INCLIN. 


PERIOD. 










e = i 




1 


Years. 


41 


Daphne. 




Goldschmidt. 


2.768 


.270 


16 45 


4.61 


42 

43 


Isis. 




Pogson. 


2.440 


.226 


8 35 


3.81 


Ariadne. 


1857 


Pogson. 


2.204 


.168 


3 27 


3-27 


44 
45 


Nysa. 




Goldschmidt. 


2.424 


.149 


3 4i 


3-77 


Eugenia. 




Goldschmidt. 


2.716 


.082 


6 34 


4.48 


46 
47 


Hestia. 




Pogson. 


2.518 


.162 


2 17 


4.00 


Melete. 




Goldschmidt. 


2.598 


.237 


'8 1 


4.19 


48 


Aglaia. 




Luther. 


2.883 


.128 


5 


4.90 


49 
50 


Doris. 




Goldschmidt. 


3.104 


.076 


6 29 


5-47 


Pales. 




Goldschmidt. 


3.086 


.238 


3 8 


5-42 


51 


Virginia. 




Ferguson. 


2.649 


.287 


2 47 


4-3i 


52 

53 


Nemausa. 


1858 


Laurent. 


2.378 


.063 


10 14 


3-67 


Europa. 




Goldschmidt. 


3.100 


.005 


7 24 


5-46 


54 


Calypso. 




Luther. 


2.610 


.213 


5 7 


4.22 


55 


Alexandra. 




Goldschmidt. 


2. 70S 


.199 


11 47 


4-55 


56 

57 
58 
59 
60 


Pandora. 




Searle. 


2.769 


•139 


7 20 


4.61 


Mnemosyne. 


1859 


Luther. 


3.160 


.107 


15 4 


5.62 


Concordia. 


i860 


Luther. 


2.698 


.o 4I 


5 2 


4-43 


Danae. 




Goldschmidt. 


2-975 


.163 


18 17 


5-13 


Olympia. 




Chacornac. 


2-7 x 5 


.119 


8 36 


4-47 


61 


Erato. 




Forster. 


3-13° 


.170 


2 12 


5-54 


62 


Echo. 




Ferguson. 


2-394 


.185 


3 34 


3-73 


§ 


Ausonia. 


1861 


DeGasparis. 


2-397 


.127 


5 45 


3-7o 


Angelina. 




Tempel. 


2.678 


.125 


1 19 


4-39 


65 


Cybele. 




Tempel. 


3-421 


.120 


3 28 


6.66 


66 


Maia. 




Tuttle. 


2.654 


■ 154 


3 4 


4-32 


67 


Asia. 




Pogson. 


2.421 


.184 


5 59 


3-77 


68 


Hesperia. 




Schiaparelli. 


2.995 


•175 


8 28 


5-19 


69 
70 


Leto. 




Luther. 


2-775 


.186 


7 58 


4.62 


Panopea. 




Goldschmidt. 


2.613 


.183 


« 39 


4.22 


7 1 
72 
73 
74 
75 


Feronia. 




Peters. 


2.266 


.120 


5 24 


3-41 


Niobe. 




Luther. 


2.756 


.174 


23 19 


4-57 


Clytie. 


1862 


Tuttle. 


2.665 


.044 


2 25 


4-35 


Galatea. 




Tempel. 


2.778 


.238 


3 59 


4.63 


Eurydice. 




Peters. 


2.670 


■307 


5 


4-36 


76 
77 


Freia. 




D'Arrest. 


3-388 


.188 


2 2 


6.24 


Frigga. 




Peters. 


2.672 


.136 


2 28 


4-37 


78 


Diana. 


1863 


Luther. 


2.623 


.205 


8 39 


4-25 


79 


Eurynome. 




Watson. 


2-443 


■195 


4 37 


3.82 


80 


Sappho. 


1864 


Pogson. 


2.296 


.200 


8 37 


3-48 


81 


Terpsichore. 




Tempel. 


2.856 


.212 


7 56 


4-83 


82 


Alcmene. 




Luther. 


2.760 


.226 


2 51 


4-59 


83 


Beatrix. 


1*865 


DeGasparis. 


2.429 


.084 


5 2 


3-79 


84 


Clio. 




Luther. 


2.367 


.238 


9 22 


3-64 


85 


Io. 




Peters. 


2.659 


.194 


11 56 


4-34 


86 


Semele. 


1866 


Tietjen. 


3.091 


.205 


4 48 


5-43 


87 


Sylvia. 




Pogson. 


3-493 


.083 


10 51 


6-53 


88 


Thisbe. 




Peters. 


2.750 


.167 


5 9 


4-56 


89 


Julia. 




Stephan. 


2-534 


.205 


15 13 


4-°3 


90 


Antiope. 




Luther. 


3-«9 


•173 


2 16 


5-5i 



TABLE IV. 



341 



NO. 


NAME. 


DISCOVERED. 


ORBIT. 


WHEN. 


BY WHOM. 


DIST. 


ECCEN. 


INCLIN. 


PERIOD. 










e = i. 




/ 


Years. 


9 1 


JEg'ma 




Stephan. 


2.496 


.066 


2 IO 


3-94 


92 


Undina. 




Peters. 


3.192 


.103 


9 57 


5-70 


93 


Minerva. 




Watson. 


2.756 


.140 


8 37 


4-58 


94 


Aurora. 




Watson. 


3.160 


.089 


8 5 


5.62 


95 


Arethusa. 


1867 


Luther. 


3.069 


.146 


12 51 


5-37 


96 


JEgle. 


1868 


Coggia. 


3-054 


.140 


16 7 


5-34 


97 


Clotho. 




Tempel. 


2.669 


•257 


« 45 


4-36 


98 


Ianthe. 




Peters. 


2.684 


.189 


15 33 


4.40 


99 


Dike. 




Borelli. 


2.797 


.238 


13 9 


4.68 


100 


Hecate. 




Watson. 


2.993 


.169 


6 10 


5.18 


101 


Helena. 




Watson. 


2-573 


■139 


10 4 


4-13 


102 


Miriam. 




Peters. 


2.663 


•254 


5 6 


4-35 


103 


Hera. 




Watson. 


2.702 


.081 


5 22 


4-44 


104 


Clymene. 




Watson. 


3.180 


.197 


2 53 


5-67 


105 


Artemis. 




Watson. 


2.380 


.176 


21 39 


3-6 7 


106 


Dione. 




Watson. 


3.201 


•195 


4 42 


5-73 


107 


Camilla. 




Pogson. 


3-56o 


.123 


9 8 


6.72 


108 


Hecuba. 


1869 


Luther. 


3-193 


.120 


4 39 


5-7i 


109 


Felicitas. 




Peters. 


2.695 


.300 


8 


4-43 


no 


Lydia. 


1870 


Borelly. 


2-733 


.077 


6 


4-52 


III 


Ate. 




Peters. 


2.592 


.105 


4 54 


4.18 


TI2 


Iphigenia. 




Peters. 


2-433 


.128 


2 36 


3.80 


"3 


Amalthea. 


187 I 


Luther. 


2.376 


.087 


5 


3-66 


114 


Cassandra. 




Peters. 


2.676 


.140 


4 54 


4-38 


"5 


Thyra. 




Watson. 


2-379 


.194 


11 36 


369 


116 


Sirona. 




Peters. 


2.767 


•143 


3 36 


4.60 


117 


Lomia. 




Borelly. 


2.991 


.023 


15 


5-i8 


118 


Peitho. 


1872 


Luther. 


2.438 


.161 


7 48 


3-Si 


119 


Althea. 




Watson. 


2.580 


.083 


5 48 


4'5 


120 


Lachesis. 




Borelly. 


3. 121 


.047 


7 


5-52 


121 


Hcrmione. 




Watson. 


3-459 


•125 


7 36 


6-43 


122 


Gerda. 




Peters. 


3-215 


.040 




5.76 


123 


Brunhilda. 




Peters. 


2.695 


.129 


6 -M 


4.43 


124 


Alcestc. 




Peters. 


2.630 


.077 


a 54 


4 -'e 


125 


Liberatrix. 




Prosp'r Henry. 


2.744 


.077 


4 36 


4-54 


126 


Velleda. 




Paul Henry. 


3.440 


.107 


2 54 


3.S1 


127 


Johanna. 




Prosp'r Henry. 


2.756 




8 18 


4.58 


128 


Nemesis 




Watson. 


2.7^1 




6 iS 


4.50 


129 


Antigone. 


l373 


Peters 


a 876 


.208 


1 .- 1 .- 


4.88 


130 


Elect ra. 




Peters. 










13, 


Vala. 




Piters. 




.08] 


4 36 




13a 


/Kthra. 




Watson. 


2.600 


.383 


•4 54 




133 


Cyrene. 




Watson. 


j.058 


,140 


- 1 ■ 




1 34 


Sophrosyne. 




1 .uthei 


8.563 


.Il8 


tl ; ■ 


4.10 


135 


Hertha. 


1874 


Peteis. 






I iS 




1 |6 


Austria. 




Palisa. 




084 






■37 


Melibaea. 




Palisa. 


3.196 


.208 


13 M 




138 


Tolosa. 




Pei rotin. 




,169 


3 >• 




'39 


| unv.i 




Watson. 




.I77 


|] Q 




140 


Siu a. 




Palisa. 




•1 • 






Ji 


ud about IOO Ot 


tiers. 













TABLE V.-ELEMENTS OF THE SATELLITES. 







MEAN 


DISTANCES. 


SIDEREAL PERIOD. 


DIAM. 






PI. = I. 


Miles. 


d. 


h. m. 


d. 


Miles. 


Mars. 














I 


Phobos. 


i-39 


5,820 




7 39 


0.32 


IO? 


2 


Deimos. 
Jupiter. 


3-48 


14,600 


1 


6 18 


1.26 


30? 


I 


Io. 


6.05 


259,000 


I 


18 28 


1.77 


2500 


2 


Europa. 


9.62 


412,000 


3 


13 14 


3-55 


2200 


3 


Ganymede. 


15-35 


658,000 


7 


3 43 


7.i5 


3700 


4 


Callisto. 
Saturn. 


26.99 


1,156,000 


16 


16 32 


16.69 


3200 


i 


Mimas. 


3-36 


115,000 




22 37 


0.94 


IOOO 


2 


Enceladus. 


4-3i 


150,000 


1 


8 53 


i-37 


? 


3 


Tethys. 


5-34 


185,000 


1 


21 18 


1.88 


500 


4 


Dione. 


6.84 


238,000 


2 


17 41 


2-73 


500 


5 


Rhea. 


9-55 


332,000 


4 


12 25 


4-5i 


I2O0 


6 


Titan. 


22.15 


770,000 


15 


22 41 


15-94 


3200 


7 


Hyperion. 


26.80 


988,000 


21 


7 7 


21.29 


? 


8 


Japetus. 
Uranus. 


64.36 

Motion 


2,254,000 

Retrograde. 


79 


7 53 


79-33 


ISOO 


i 


Ariel. 


7-44 


119,000 


2 


12 28 


2.52 


? 


2 


Umbriel. 


IO.37 


166,000 


4 


3 27 


4.14 


? 


3 


Titania. 


17.OI 


272,000 


8 


16 55 


8.71 


? 


4 


Oberon. 
Neptune. 


22.75 
Motion 


364,000 

Retrograde. 


13 


11 6 


13.46 


? 


1 


Satellite. 


I2.00 


210,000 


5 


21 8 


5.87 


? 



(342) 



INDEX 



Note. — Figures refer to pages. 



Aberration of light, 276. 
Adams, a discoverer of Neptune, 

243- 
Aerolites, 270. 

Air, is there at the moon? 186. 
Airy, on mass of earth, 90, 334. 
Alcor, 319. 

Alcyone, 299, 308, 319. 
Aldebaran, 319. 
Algol, 276, 293, 320. 
Alpha Arietis, 320. 

Centauri, light of, 289 ; 

distance of, 290; orbit of, 
296-298. 

Alpheratz, 321, 326. 

Altair, 325. 

Altitude, 14; how measured, 46; 
true, 69; affected by paral- 
lax, 96. 

and azimuth instrument, 

Amplitude, 13; ol sunrise, 72. 
Andromeda, 321 ; nebula in, 300, 

3° 2 ' 
Angle, of ecliptic and equinoc- 
tial, 33. 

the visual, 36. 

Antares, 291, 202, 324. 
Aphelion, 10S, 255. 
Apogee, io8. 

Apparition, circle of perpetual, 

27, 20. 
Appulse, lunar, io.|. 
Apsides, 10S, 1 19 ; o[ moon's 

orbit, 177. 



Aquarius, 326. 

Aquila, 325. 

Arago, analysis of sunlight, 161. 

Arc, diurnal, 70. 

Arcturus, 282, 322. 

Argo, 322. 

Ariel, a satellite of Uranus, 242. 

Aries, 25, 320. 

Aristarchus of Samos, 133. 

Ashy light of the moon, 181. 

Aspects of the planets, 135. 

Astral systems, 300. 

Astrology, 10. 

Astronomical instruments, 34. 

Astronomy defined, 10. 

Atmosphere, height of, 74; o( 

sun, 166; of Mercury, 21S; 

o\ Venus, 220. 
Attraction, external, affecting 

shape o\ earth. 204. 
of gravitation, 8i : laws 

oi\ $2\ o( sun as influencing 

moon's orbit. 1 70. 

August meteors, 268, 

Auriga, 320. 

Aurora Borealis, 150. 

Axis, o\ a circle, o\ the horizon, 
12 ; o\ the earth, 18 ; o\ the 
hea\ ens, 23 ; of a lens. ;^ ; 
o( a telescope, 43 ; o\ an 
ellipse. 98; of earth as affect- 
ing change o( seasons, 111 ; 

o( the sun, 1 55 ; of a conic 

section, 254. 

Azimuth, 13, 2^. 



34 ■ 



Bad 



INDEX. 



Cor 



Bache, A. D., measuring appa- 
ratus, 78. 

Baily's beads, 198. 

Ball, brothers, saw streak divid- 
ing rings of Saturn, 237. 

Bayer, named stars by letters, 
285. 

Bearing of a star, 13. 

Beehive, the, 321. 

Beer and Madler's map of the 
moon, 182. 

Bellatrix, 320. 

Belts of Jupiter, 231. 

Berenice's hair, 323. 

Betelgeuze, 320. 

Biela's comet, 260, 269. 

Binary stars, 295. 

Bolides, 269. 

Bond, discovered Saturn's gray 
ring, 237. 

Bootes, 322. 

Boston and Providence R. R., a 
base of triangulation, 78. 

Bradley, discovered aberration 
of light, 276. 

British association's map of 
moon, 182. 

Caesar, Julius, reformed the cal- 
endar, 125. 
Calendar, the, 124-126. 
Callisto, a satellite of Jupiter, 

233- 
Camelopard, 319. 
Cancer, 321. 

tropic of, 113, 320. 

Canes Venatici, 323 ; nebula in, 

301. 
Canis Major, 322; Minor, 321. 
Capella, 320. 
Capricornus, 325. 
Cassini, J. D., plan of Mars' 

path, 132; observation of 

Mercury, 138. 
Cassiopeia, 319; new star in, 

292. 
Castor, 321. 

Cavendish, on earth's mass, 89. 
Celestial motion, general law of, 

254. 
Centaurus, cluster in, 299. 
Cepheus, 319. 



Ceres discovered, 227. 

Cetus, 320, 326. 

Change of seasons, 109. 

Chicago, tide at, 210. 

Chinese records of comets, 247 ; 
of stars, 292. 

Chromosphere of sun, 170. 

Chronograph, 44. 

Chronometer, 60. 

Circle, vertical, 12; great, 12; 
of daily motion, 23, 69; of 
perpetual apparition or oc- 
cultation, 27; mural, 46; 
meridian, 49; hour, 57; day, 
112; polar, 113, 114. 

Circumference of earth, 17, 26. 

Circumpolar bodies, 27. 

Clairaut, predicted the return of 
Halley's comet, 258. 

Cleanthes of Assos, 133. 

Clock, astronomical, 56. 

Clouds, the Magellanic, 308, 

Clusters of stars, 299. 

Coal sack, the, 304. 

Collimation, line of, 42. 

Color of stars, 292. 

Colures, the, 33 ; the solstitial, 64. 

Coma, part of comet, 248. 

Combustion theory of solar heat, 
171. 

Comets, 247; parts of, 248; are 
material, 248 ; apparent di- 
mensions of, 249 ; actual di- 
mensions, 250; tail, 251; 
orbits of, 253 ; elements of, 
255; how recognized, 257; 
of long period, 257; of short 
period, 259; double, 260; 
danger of collision with, 261 ; 
Halley's, 257; Lexell's, 261 ; 
Donati's, 263; of 1843, 26 ~3 5 
of 1861, 263; of 1880, 264; 
how produced, 315. 

Cone, 253 ; sections of, 254. 

Conjunction, 134; of moon, 174. 

Constellations, 283, 317-327. 

Contraction theory of solar heat, 
172. 

Co-ordinates, 13, 56. 

Copernicus, 18, 133, 214. 

a lunar mountain, 183. 

Cor Caroli, 323. 



Cor 



INDEX. 



Eve 



Cor Hydrse, 322. 

Corona, the solar, 164; nature 

of, 166. 
Corvus, 323. 
Co-tidal lines, 208. 
Crater, 323. 
Craters, lunar, 183. 
Crepuscular curve, 74. 
Culmination, 29, 43 ; time of, 

57, 65. 
Cyclones, solar, 156. 
Cygnus, 325. 

Dawn, the, 73. 

Day, the solar, 55 ; civil, 56; side- 
real, 56; and night, relative 
length of, in different places, 
69 ; dark, 272. 

circle, 112. 

Declination, 24, 64; how ob- 
served, 58 ; of the sun, 330. 

Deimos, a satellite of Mars, 224. 

De Lisle's method of discussing 
transits of Venus, 143. 

Deneb, 321. 

Denebola, 322. 

Density, of the earth, 90; of 
heavenly bodies, how found, 

151. 

Diagrams, their use in astron- 
omy, 109, 197. 

Diameter of earth, 17, 81; of 
heavenly bodies, how found, 
147. 

Dione, a satellite of Saturn, 240. 

Dip of horizon, 9. 

Dipper, the, 319. 

Direct motion, 128. 

Distance, of the moon, 93; of 
an inferior planet, 139; of 
planets from the sun, [39 ; 
of a superior planet, 140; of 
a larger fixed star, 288; of a 
telescopic star, 290. 

Diurnal are, 70. 

Dolphin, the, 325. 

Donati's comet, 203. 

Double stars, 21)4; revolution o\\ 
200. 

Draco, 310; nebula in, 301 

Dumb-bell nebula. j,o2. 

Dust, meteoric, 2^2. 



Earth, shape of, 15, 80; diame- 
ter, 16, 26, 81; rotates, 17; 
rotation made visible, 19; 
interior fluid, 85 ; mass found, 
88; density, 90; moves about 
sun, 101 ; orbit, 103, 108, 
119; ratio of motion, 104; 
mean distance from sun, 150; 
falls toward the sun, 150; 
shadow of, 193; shape af- 
fected by external attraction, 
204; as a planet, 221. 

Eccentricity of an ellipse, 99 ; of 
earth's orbit, 108; ib. dimin- 
ishing, 119; of moon's orbit, 
176; of comet's orbit, 257. 

Eclipses, of moon, 193; of sun, 
197; possible number in one 
year, 199; phenomena of, 
163, 198; of Jupiter's satel- 
lites, 234, 275 ; solar of 1868, 
167. 

Ecliptic, the, 33, 63 ; signs of, 
117; limits of latitude, 332; 
of longitude, 334. 

Ellipse, the, 97, 254. 

Elliptical orbit of the earth, how 
found, 103. 

Elongation, 139. 

Enceladus, a satellite of Saturn, 
240. 

Encke's calculations of parallax 
of the sun, 146. 

Encke's comet, 259. 

Epping base of triangulation, 78. 

Equation of time, 1 19-122 ; table 
of, 335- 

Equator, the terrestrial, iS; the 
celestial, 23. 

Equatorial mounting o( tele- 
scone. 52. 

Equinoctial, the, 23; meridian 
altitude of, 32S. 

Equinox, the vernal, 25. 

Equinoxes. 31; precession o\\ 
1 18, 284, 330. 

Eratosthenes, record of stars in 

Scorpio. 201. 

Eridanus, 320. 
Establishment of port. 208. 

Europa, a satellite of J upiiei . 233. 
Evening star. 1 20. 



Exp 



INDEX. 



Hyp 



Experiments, of Foucault, on 
earth's rotation, 19; of Mas- 
kelyne, on mass of earth, 88 
of Cavendish, on same, 89 
of Airy, on same, 90; to il 
lustrate rings of Saturn, 240 
of Fizeau, on velocity of 
light, 278 ; of Plateau, on 
rotating oil, 315. 

Faculae, 159; theories of, 170. 
Falling body, motion of, 148. 
Faye's comet, 260. 
Fire Island, base of triangula- 

tion, 78. 
Fixed stars, 63, 281 ; they are 

suns, 286. 
Fizeau's experiment on light, 

278. 
Focus, of a lens, 35 ; of a mirror, 

39; of an ellipse, 98; of a 

conic section, 254. 
Fomalhaut, 326. 
Force, laws of, 105. 
Forces, radial and tangential, 

83- 
Foucault's experiment with a 

pendulum, 19; on velocity 

of light, 280. 
Fraunhofer's lines, 162. 
Frequency of eclipses, solar, 199 ; 

lunar, 200. 
Full earth, as visible from the 

moon, 181. 



Galaxy, the, 303 ; theories of, 
305- 

Galileo, his recantation, 18; dis- 
covered moons of Jupiter, 
231 ; discovered rings of Sat- 
urn, 236. 

Gambart's comet, 260. 

Gama Virginis, 296. 

Ganymede, a satellite of Jupiter, 

233- 
Gemini, 321. 
Geology, lessons of, 312. 
Georgium Sidus, 241. 
Globe, celestial, 58, 317 ; of glass, 

cracked by expansion, 185. 
Golden number, the, 202. 



Gravitation, attraction of, 81 ; 
measure of, 149 ; obeyed by 
the moon, 150; affecting the 
shape of the earth, 204. 

Great lakes, tides of, 210. 

Gyroscope, the, 22. 

Hall, A., discovered satellites of 

Mars, 224. 
Halley, his method of finding 

the solar parallax, 143 ; his 

comet, 257. 
Harmonies of the solar system, 

312. 
Harvest-moon, the, 190. 
Head of comet, 248, 253. 
Heat and motion correlative, 171, 

313- 

Heat, of summer, causes of, 116; 
maximum of, 117; of sun, 
169; theories of solar, 171. 

Heavens, center of, 9, 109. 

Hemispheres, northern and 
southern, 18. 

Hercules, 308, 324; cluster of 
stars in, 299. 

Herschel T. (Win.), his telescope, 
40 ; discovered Uranus, 241 ; 
theory of the galaxy, 305 ; 
star-gauging, 305 ; investi- 
gated the motion of the solar 
system, 307 ; advanced the 
nebular hypothesis, 316. 

II. (J. F. W.), opinion of 

orreries, 245 ; of constella- 
tion figures, 317. 

Hesperus, 129. 

Hipparchus, his catalogue of 
stars, 286. 

Horizon, the visible, 9 ; dip of, 
real, 10, 25. 

Hour-circles, 57. 

Humboldt's account of star- 
showers, 265. 

Hunter's-moon, 191. 

Huyghens, discovered Saturn's 
rings, 236. 

Hyades, the, 319. 

Hydra, 322. 

Hyperbola, 254. 

Hyperion a satellite of Saturn, 
240. 



346 



Ima 



INDEX. 



Mea 



Image, refracted, 36; reflected, 

39- 

Inclination of orbit of comet, 
256. 

Inertia, 105 ; delays the tide, 208. 

Inferior planet, 134; distance of, 
how found, 139. 

Inner group of planets, coinci- 
dences of, 225. 

Intra-mercurial planet, 214. 

Io, a satellite of Jupiter, 233. 

Irradiation, effect of, 220. 

Japetus, a satellite of Saturn, 
240. 

Julian calendar, 125. 

Jupiter, sidereal revolution found, 
137; diameter of, 147, 233; 
mass, density, 151 ; described, 
231-234; belts of, 231; re- 
semblances to the sun, 233 ; 
moons of, 233 ; attraction for 
Lexell's comet, 261. 

satellites of, 233 ; longi- 
tude by, 61 ; motion of light 
by, 275. 

Kepler, proves theory of solar 
system, 133; laws, first and 
second, 105; third, 141. 

Kirchhoff's laws of spectrum 
analysis, 163. 

Lacaille, observation on twilight, 

74- 

Lalande, unrecognized observa- 
tions of Neptune, 244. 

La Place, favored the nebular 
hypothesis, 316. 

Lassell, discovered satellites of 
Uranus, 242. 

Latitude, terrestrial, 19,25; how 
found, 69 ; equal to altitude 
of pole, 26; length of degree, 
26 ; celestial, 64. 

Laurentian meteoroids, 268. 

Laws of Kepler, first and second, 
105; third, 141. 

Le Gentil's voyage to India. 

143- 

Lemonnier, unrecognised obser- 
vations of Uranus, 241. 



Lens, 35 ; convex, 36. 

Leo, Major, 321 ; radiant of No- 
vember meteoroids, 266; Mi- 
nor, 323. 

Lepus, 320. 

Letters, used to name stars, 285. 

Leverrier, a discoverer of Nep- 
tune, 243. 

Lexell's comet, 261. 

Libra, 324. 

Librations of moon, 187. 

Light, analysis of, 163; the zodi- 
acal, 272 ; progressive motion 
of, 275; aberrations of, 276; 
Fizeau's experiment on, 278; 
of distant stars, 291, 

Line of collimation of telescope, 
42. 

Longitude, terrestrial, 19, 25; 
found by telegraph, 60; by 
chronometer, 60; by eclipses 
of Jupiter's satellites, 61 ; by 
lunar observations, 61 ; celes- 
tial, 64; of perihelion of 
comet, 256. 

Lucifer, 129. 

Lunar observations, 61. 

Lunation, 174. 

Lynx, 319. 

Lyra, 323; nebula in, 301. 

Miidler, theory of the galaxy, 

306. 
Magellanic clouds, 308. 
Magnitudes of stars, 281. 
Map of the moon's surface, 1S2; 

of Mars, 223. 
■ stellar, 317; the circum- 

polar, 31S. 
Maraldi's observation on Mars, 

142. 
Mars, 131: mini o\\ as drawn 

b\ Cassini, 132, 133; parallax 

of, [42; appearance, 222; 

rotation, 223 ; orbit of, 224 j 

satellites o\\ 22.1. 
Maskelyne's experiment on mass 

o\ earth. SS. 
Mass, o\ earth, SS ; o\ 

body, how found. 

o( Mat's. 298, 

Mean solar tune. [21, 



heavenly 
14S 151; 



347 



Med 



INDEX. 



Oct 



Mediterranean, tides of, 210. 

Medium, resisting, indicated by 
comets, 259. 

Mercury, 130; transits of, 130, 
216; described, 214. 

Meridian, the celestial, 13,23; 
terrestrial, 18 ; plane of, 28. 

circle, 49. 

Meteoric astronomy, 265 ; show- 
ers, 265 ; theories of, 269 ; 
dust, 272 ; theory of solar 
heat, 171. 

Meton, discovered golden num- 
ber, 202. 

Micrometer, the, 47. 

Microscope, the, 36. 

Milky way, 303. 

Mimas, a satellite of Saturn, 240. 

Minor Planets, discoveries of, 
227 ; characteristics of, 228 ; 
origin of, 229 ; method of 
naming and symbolizing, 229. 

Mira, 293, 320. 

Mirror, 39. 

Mitchel, O. M., method of obser- 
vation, 45. 

Mizar, 319. 

Monoceros, 322. 

Montpellier, observations at, on 
rainy days, 211. 

Moon, the distance of, 93 ; par- 
allax, diameter, 94; volume 
of, 95; orbit of, 96; a pro- 
jectile, 149; periods of revo- 
lution, 174; path curved 
towards the sun, 175; mo- 
tions of, practically illus- 
trated, 179; phases of, i8:>; 
ashy light of, 181 ; appear- 
ance in the telescope, 182; 
mountains of, 182; maps of, 
182; active volcanoes in, 186; 
inhabitable, 186; rotation of, 
187; librations of, 187; runs 
high or low, 189; harvest, 
190; light and heat of, 191 ; 
visibility of objects on, 191 ; 
eclipses of, 193; visible when 
eclipsed, 195 ; occultation of 
star by, 197; causes tides, 
204; causes clouds or rain, 
211 ; wet and dry, 212. 



Morning and afternoon unequal, 
124. 

Morning star, 129. 

Motion, of earth imperceptible, 
18; among the stars, 62; 
compound, 105 ; curvilinear, 
106 ; direct and retrograde, 
128, 131 ; of falling body, 
148 ; laws of celestial, 254 ; 
and heat correlative, 171, 
313; of solar system, 307. 

Mountains of the moon, 182. 

Munich, observations at on rainy 
days, 211. 

Mural circle, 46; how adjusted, 



Nadir, the, 12. 

Names of minor planets, how 

given, 229. 
Nature of fixed stars, 286. 
Nebulae, 300; double, 303. 
Nebular hypothesis, 229, 311; 

stated, 313 = 
Nebulous stars, 303. 
Neptune, discovery of, 243 ; ap- 
pearance of, 244; satellite 

of, 245. 
New stars, 292. 
Newton, I., telescope, 41 ; law 

of gravitation, 83 ; law of 

celestial motion, 254. 
Node, of moon's orbit, 178; of 

comet's orbit, 255. 
Noon, mean and apparent, 56. 
Northern Crown, 323; new star 

in, 293. 
November meteoroids, 265 ; orbit 

of, 267. 
Nucleus of solar spot, 157; of 

comet, 248. 



Oberon, a satellite of Uranus, 
242. 

Object-glass, 38. 

Observatory, National, at Wash- 
ington, 47. 

Occultation, circle of perpetual, 
27 ; of stars by moon, 197. 

Octants, of moon, 174. 



348 



Olb 



INDEX. 



Red 



Olbers's theory of the minor 
planets, 229. 

Ophiuchus, 324; new star in, 
293 ; double star in, 295, 296. 

Opposition, 134; of moon, 174. 

Orbit, of earth, how found to be 
elliptical, 103 ; of comet, 255 ; 
elements of comet's, 256. 

Orion, 320; nebula in, 300. 

Orrery, Herschel's, 245 ; value 
of, 245. 

Outer group of planets, coinci- 
dences in, 246. 



Parabola, the, 254. 

Parallax, 92 ; of the moon, 93 ; 
horizontal, 95; effect of on 
altitude, 96; of sun, 100, 
146; of a planet, 147. 

Parallels of latitude, 19. 

Path of the sun, 31. 

Pegasus, 321 ; square of, 326. 

Pendulum, 86; experiment with 
on earth's mass, 90; Fou- 
cault's, 19. 

Penumbra, of solar spot, 157; 
of earth's shadow, 195; of 
moon's shadow, 197. 

Perigee, 108. 

Perihelion, 108, 119, 255; dis- 
tance of comet, 257. 

Periodic stars, 293. 

Periodicity of sun-spots, 159. 

Perseus, 320; radiant of August 
meteors, 269. 

Phases, of moon, 180; of Mer- 
cury, 215; of Venus, 218. 

Philolaus, 133. 

Phobos, a satellite of Mars, 
224. 

Photosphere of the sun, 170. 

Pisces, 326. 

Piscis Australis, 326. 

Plane, of horizon, 0; of merid- 
ian, 28 ; of ecliptic, 33, 109, 

Planets, 63, 1 28, 214; inferior 
and superior, 134 ; distance 

of inferior, how found, 139 ; 

oi superior, how found, [40; 
distances from the sun, 141 ; 
size of, [48; coincidences of 



inner group of, 225 ; minor, 

226, 339 ; coincidences of 

. outer group of, 246; elements 

of, 33&- 

Plateau's experiment on motion, 

315- 

Pleiades, the, 299, 319. 

Plumb-line, perpendicular to 
the horizon, 12; does not 
point to center of the earth, 
86. 

Point, how located, 13. 

Pointers, the, 319. 

Polar circle, 113. 

distance, 24. 

Polaris, 26, 282. 319. 

Polariscope, 161, 253. 

Poles, of a circle, of the horizon, 
12; of the earth, 18; of 
heavens, 23 ; the north, 26 ; 
of the ecliptic, 64; altitude 
of the celestial, how found, 
65 ; of the galaxy, 305. 

Pollux, 321. 

Pons's comet, 258. 

Pores of the sun's surface, 160. 

Praesepe, 299, 321. 

Precession of the equinoxes, 118, 
284, 330. 

Prime vertical, 13. 

Priming and lagging of the tide, 
209. 

Procyon, 321. 

Projectile, motion of, 148. 

Public surveys, 76. 

Pulkova, observatory at, 41. 

Quadrature, 135; of moon, 174. 

Radiant, of November meteors, 

266; oi August meteors. 

269. 
Radius of earth's orbit a unit 

i^\~ measure. 130. 
vector, 98; o\ a planet 

describes equal areas in equal 

times, 320. 
Railroad transit. 52. 
Rain not influenced by the moon. 

211. 
Red prominences of the sun. 164 : 

theories of, 171. 



Ref 



INDEX. 



Sta 



Reflection, 39. 

Refraction, 34; atmospheric, 66. 

Regulus, 321. 

Resultant of forces, 106. 

Reticule, 43, 45. 

Retrograde motion, 131, 315. 

Revolution, sidereal and synodic, 

136. 

Rhea, a satellite of Saturn, 
240. 

Rigel, 320. 

Right ascension, 25, 64; how 
observed, 58. 

Rilles in the moon, 185. 

Rings of Saturn, 236-239; neb- 
ular theory as to, 314. 

Romer, discovered motion of 
light, 275. 

Rosse, Lord, telescope of, 42. 

Rotation, of earth, 17; made vis- 
ible, 19; affecting shape of 
earth, 204; of sun, 155; of 
moon, 187 ; of Mercury, 217 ; 
of Venus, 220 ; of Mars, 223 ;' 
of Jupiter, 232 ; of Saturn, 
236 ; of Uranus, 242 ; of 
Neptune, 244. 

Royal zone of sun, 156. 



Sagittarius, 325. 

Saidak, 319; a proof of distinct 
vision, 292. 

Saros, the, 201. 

Satellites, of Venus, 221 ; of 
Mars, 224 ; of Jupiter, 233 ; 
longitude found by, 61 ; mo- 
tion of light by, 275 ; of Sa- 
turn, 240 ; of Uranus, 242 ; 
of Neptune, 245 ; table of 
elements of, 342. 

Saturn, appearance of, 235 ; 
rings of, 236; satellites of, 
240. 

Scorpio, 324. 

Sea-level, 85. 

Seasons, change of, 109; length 
of, 118; variations in, 119; 
at Mars, 223. 

Seconds of arc, how measured, 
48. 

Serpens, 323. 



Serpentarius (or Ophiuchus), 
324; new star in, 293. 

Sextant, the, 61, 328. 

Shadow of earth, 193 ; of moon, 
197 ; rate of motion of in an 
eclipse of the sun, 199. 

Shooting stars, 265 ; height and 
velocity of, 266; nature of, 
267. 

Sidereal, day, 56 ; time, has no 
equation, 120; revolution, 
136. 

Signs, of ecliptic, 117; of zodiac, 
284. 

Sirius, 321; magnitude, 282; 
light of, 288. 

Sky, the, 10 ; apparent revolu- 
tion of, 17 ; as seen from the 
pole, 25 ; from the equator, 
26 ; center of the, 109. 

Solar eclipse, 163, 197, 199. 

heat, 169; origin of, 171. 

spots, 154; dimensions of, 

158; periodicity, 159; de- 
pressions in surface of sun, 
161 ; theories of, 170. 

system, motion of, 307 ; 



harmonies of, 312. 

time, 55, 121. 

Solstices, 32; summer, 113; 

winter, 114. 
Spectrum analysis, 162, 300. 
Speculum for telescope, 40. 
Sphere, 11. 
Sphericity of earth, how shown, 

15- 

Spica, 323. 

Star-gauging, 305. 

Stars, how located, 25, 56; hour- 
ly motion of, 56 ; fixed, 63, 
281; shooting, 265; de- 
scribed, 281-309; magni- 
tudes, 282 ; number of, 282 ; 
indicated by letters, 285 ; 
catalogues of, 286 ; nature 
of, 286 ; distance of, 288 ; 
variations of, 291 ; have van- 
ished, 292; new, 292; period- 
ic, 293 ; double, 294 ; binary, 
295 ; multiple, 297 ; clusters 
of, 299 ; nebulous, 303. 

Star showers, 265. 



Str 



INDEX. 



Vel 



Streamers, luminous, of sun, 164. 

Summer heat, causes of, 116; 
changes in, 119. 

Sun, the, shadow of at noon, 30; 
annual motion of, 63; disc 
distorted by refraction, 67 ; 
parallax of, 100, 146; motion 
of, apparent only, 101 ; di- 
ameter of, 147; mass of, 151 ; 
density of, 152; power of, 
152; physical nature of, 154; 
spots on, 154; axis of, 155; 
royal zone, 156; faculse, 159; 
mottled surface of, 160; evi- 
dence of polariscope respect- 
ing, 161 ; evidence of spec- 
trum analysis concerning, 
162; phenomena of eclipses 
of, 163 ; corona and red 
prominences, 166; light and 
heat of, 168; eclipses of, 
197; causes tides on the 
earth, 206; theories concern- 
ing, 169. 

and moon, apparent size, 

68. 

light, analysis of, 162; in- 
tensity of, 168. 

Superior planets, 134; distance 
of, how found, 140. 

Surveys, public, 76. 

Synodic revolution, 136; table 
of planetary, 141 ; of moon, 
174. 

Syzigies of moon, 174. 

Tail of comet, 248; how caused, 
251; curvature of, 251; is 
hollow, 252. 

Taurus, 319; nebula in, 302. 

Telegraph, used in observing 
transits, 44; to find longi- 
tude, 60. 

Telescope, the, 34; refracting, 
38 ; refleel ing, 40 ; equato- 
rial, 52. 

Terminator of the moon, 1 82. 

Tethys, a satellite oi Saturn. 240. 

Theodolite, 51. 

Theories, of tin- sun's nature, 
100 ; of solar heat, 171; ol 
minor planets, 229 ; of mo- 



teoroids, 269; of the zodiacal 
light, 273 ; of periodic stars, 
294 ; of the galaxy, 305 ; the 
nebular hypothesis, 311. 

Theta Orionis, 297. 

Tides, defined, 203 ; caused by 
sun and moon, 204 ; causes 
of, explained, 204; variations 
of, explained, 207 ; delayed 
by inertia, 208 ; priming and 
lagging of, 209 ; origin of 
tide-wave, 209; primitive and 
derivative, 210; in the Medi- 
terranean, 210; in the Great 
Lakes, 210; in the air, 211. 

Time, 55; mean solar, 55, 121; 
sidereal, 56 ; equation of, 
119, 121; tables of, 335>33 6 - 

Titan, a satellite of Saturn, 240. 

Titania, a satellite of Uranus, 
242. 

Titius, series of, 226 ; is not ap- 
plicable to Neptune, 245. 

Toaldo, observed influence of 
moon on weather, 212. 

Transit of a star, 43 ; of an infe- 
rior planet, 130; of Mercury, 
216; of Venus, 143, 219; of 
satellites of Jupiter, 234. 

instrument, 43 ; railroad, 

52. 

Triangulation, 77. 

Tropic of Cancer, 113; of Capri- 
corn, 115. 

Twilight, 73. 

Tycho Brahe, 131. 

Tycho, lunar mountain, 1S4. 

Umbra, of solar spot. 157; of 
earth's shadow. 103. 

Umbriel, a satellite of Uranus, 
242. 

Units of time. 55. 

Uranus, discovery oi\ 241 ; ap- 
pearance, 24] : satellites of. 
242. 

Ursa Major, ;i S. 

Minor. 310. 

Vega, 325. 

Velocity, angular compared with 

linear, [02. 



35' 



Ven 



INDEX. 



Zon 



Venus, 129, 218; sidereal revo- 
lution of, 138; distance from 
sun, 140; diameter, 147; 
transit of, 143, 219; atmos- 
phere of, 220 ; satellite of, 
221. 

Vernal equinox, 25. 

Vertex, of a conic section, 254. 

Vertical circle, 12. 

the prime, 13. 

Visual angle, the, 35. 

Volcanoes, lunar, 186. 

Volumes 'of heavenly bodies, 
how found, 148. 

Walker, Sears C, perfected dis- 
covery of Neptune, 244. 

Washington, observatory at, 47. 

Water at the moon, 186. 

Watson, his supposed intra-mer- 
curial planet, 214. 



Weather not influenced by the 

moon, 212. 
Weight at equator and at poles 

of earth, 86. 

Year, the measure of, 29, ^ ; the 
tropical, 124; the sidereal, 
124; the anomalistic, 125; 
table of, 336. 

Young, C. A., discussion of the 
solar parallax, 146. 

Zenith, 12; the true, 87. 

distance, 14. 

Zeta Cancri, 297. 
Zodiac, the, 129, 284. 
Zodiacal light, the, 272. 
Zollner, on magnitudes of stars, 

282. 
Zone, 115; royal, of the sun, 

156. 



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PLATE VI.-Horizon at Midnight, Sept. 23; at 10 P. M., Oct. 23; at 8 p. m., Nov. 



PLATE VII.-Hor 



iton at Midnight, Nov. it; at to p M . Dec, u; .u s r. m . ha, ,j 




PLATE VIII.— Horixoi 



March 




PLATE [X.— Horiion at Midnight, March ti 



M . April 10: it S P \' M 



I . \ . ^Pus 



PLATE X.— Horizon at Midnight, Mayix; at 



to P. M. t linn- .-i : .it S r v.. lulv ::. 




PLATE XI.— Horizon :<t Midnight, July 




PLATE XII. — Hori/on at Midnight, Sept. .- • ; .»t M r. m., Oct, 1 1 ; 



.it B r. m., Nov. H 



LIBRARY OF CONGRESS 




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